From bb5de7aa0402ffecddb77543be52124b275239df Mon Sep 17 00:00:00 2001
From: GitHub CI Documentation builder This is the complete list of members for BslAdvection1D< IDimInterest, AdvectionDomain, FunctionDomain, AdvectionFieldBuilder, AdvectionFieldEvaluator, TimeStepper >, including all inherited members. A class which computes the advection along the dimension of interest IDimInterest.
+ More... A class which computes the advection along the dimension of interest IDimInterest. This operator solves the following equation type \( \partial_t f_s(t,x) + A_{s, x_i} (x') \cdot \partial_{x_i} f_s (t, x) = 0, \qquad x\in \Omega, x'\in\Omega'\) with The characteristic equation is solved on the advection domain \( \Omega'\). Then the feet on \( \Omega\) are computed from the characteristic feet on \( \Omega'\) and the function \( f \) is interpolated at the feet in \( \Omega \). The characteristic equation is solved using a time integration method (ITimeStepper). Constructor when the advection domain and the function domain are different. When AdvectionDomain and FunctionDomain are different, we need one interpolator for each domain. We can also use it when we want two differents interpolators but defined on the same domain (e.g. different boundary conditions for the evaluators). Advects allfdistribu along the advection dimension IDimInterest for a duration dt.
\[ \frac{df_s}{dt}= q_s \sqrt{\frac{m_e}{m_s}} E \frac{\partial f_s}{\partial v} \]
The purpose of the BslAdvection1D operator is an advection along a given direction of the phase space. The advection field is given as input. The dynamics of the motion are governed by the following equation.
+\[ \partial_t f(t,x) + A\partial_{x_i}(x')f(t,x) = 0, \qquad x \in \Omega, x' \in \Omega', \]
+ with Here are some examples of equation types the BslAdvection1D operator can solve:
+\[ \partial_t f(t,x) + A_x(x)\partial_{x}f(t,x) = 0, \qquad x \in \Omega, \]
+
+\[ \partial_t f(t,x,y) + A_x(x,y)\partial_{x}f(t,x,y) = 0, \]
+
+\[ \partial_t f(t,x,y,v_x,v_y) + A_x(x,y)\partial_{x}f(t,x,y,v_x,v_y) = 0, \]
+
+\[\begin{aligned} & \partial_t f(t,x,v_x) + A_x(x,v_x)\partial_{x}f(t,x,v_x) = 0, \qquad \text{ with for instance, } A_x(x,v_x) = v_x, \\ & \text{or } \partial_t f(t,x,v_x) + A_{v_x}(x,v_x)\partial_{v_x}f(t,x,v_x) = 0, \qquad \text{ with for instance, } A_{v_x}(x,v_x) = E(x), \end{aligned} \]
+
+\[\begin{aligned} & \partial_t f_s(t,x,v_x) + A_{s,x}(x)\partial_{x}f_s(t,x,v_x) = 0, \end{aligned} \]
+ The operator takes as templated parameters: Remark/Warning: the BslAdvection1D operator is built with builder and evaluator for the advection field and interpolator for the function we want to advect. Theses operators have to be defined on the same domain as the advection field and function. For instance, if the advection field and/or the function are defined on the species dimension, then the interpolators have to contain the species dimension in its batched dimensions (see tests in the Remark/Warning: The advection field need to use interpolation on B-splines. So we cannot use other type of interpolator for the advection field. However there is no constraint on the interpolator of the advected function. CAnalyticalInvertibleCurvilinear2DToCartesian A class for describing analytical invertible curvilinear 2D mappings from the logical domain to the physical domain
- ►CBernsteinPolynomialBasis
- CBslAdvectionRP Define an advection operator on 2D \((r, \theta)\) domain
- CBslAdvectionSpatial A class which computes the spatial advection along the dimension of interest DDimX
- CBslAdvectionVelocity A class which computes the velocity advection along the dimension of interest DDimV
- CBslExplicitPredCorrRP A second order explicit predictor-corrector for the Vlasov-Poisson equations
- CBslImplicitPredCorrRP A second order implicit predictor-corrector for the Vlasov-Poisson equations
- CBslPredCorrRP Predictor-corrector for the Vlasov-Poisson equations
- CBSplinesP
- CBSplinesR
- CBSplinesVp
- CBSplinesVr
- CBSplinesVx
- CBSplinesVy
- CBSplinesX
- CBSplinesY
- CBumpontailEquilibrium A class that initializes the distribution function as a sum of two Maxwellian functions
- Ccartesian_product_impl
- Ccartesian_product_impl< std::tuple< std::tuple< HeadArgs... >, TailTuples... >, OutTupleOfTuples >
- Ccartesian_product_impl< std::tuple<>, OutTupleOfTuples >
- CCartesianSolution Define a Cartesian solution of the Poisson equation
- CCartesianToBarycentricCoordinates
- CChargeDensityCalculator A class which computes charges density with Kokkos
- CCircularToCartesian A class for describing the circular 2D mapping
- CCollisionsGuard Header Guard for collision operator
- CCollisionsInter Class describing the inter-species collision operator
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- ►CCollisionsIntra Class describing the intra-species collision operator
- CCollisionSpVparMu A class which computes the collision operator in (vpar,mu)
- CConstantFluidInitialization A class that initializes a fluid species with constant moments
- CConstantRate A class that describes a reaction rate that is constant
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- ►CCosineEvaluator
- CCrankNicolson A class which provides an implementation of a Crank-Nicolson method
- CCurvilinear2DToCartesian A class for describing curvilinear 2D mappings from the logical domain to the physical domain
- CCurvilinearSolution Define a curvilinear solution of the Poisson equation
- CCzarnyToCartesian A class for describing the Czarny 2D mapping
- CDecentredRotationAdvectionFieldSimulation Simulation of a decentred rotated elipse-type function
- CDecentredRotationSimulation Simulation of a decentred rotated elipse-type function
- CDerivField
- CDerivField< ElementType, ddc::DiscreteDomain< DDims... >, NDerivs, Allocator > A class which holds a chunk of memory describing a field and its derivatives
- CDerivFieldCommon
- CDerivFieldCommon< ChunkType, ddc::DiscreteDomain< DDims... > > An abstract class which holds a chunk of memory describing a field and its derivatives
- CDerivFieldSpan
- CDerivFieldSpan< ElementType, ddc::DiscreteDomain< DDims... >, LayoutStridedPolicy, MemorySpace > A class which holds references to chunks of memory describing a field and its derivatives
- CDiffusiveNeutralSolver A class that solves a so-called "pressure-diffusive" fluid neutral model
- CDimX_pC Tag the first non periodic dimension in the pseudo_Cartesian domain
- CDimY_pC Tag the second non periodic dimension in the pseudo_Cartesian domain
- CDiocotronDensitySolution The diocotron exact solution of the density \( \rho \)
- CDiscreteSubDomain A class which describes a collection of ddc::DiscreteElements which form a subdomain
- CDiscreteSubDomainIterator An iterator type for the DiscreteSubDomain
- CDiscreteToCartesian A class for describing discrete 2D mappings from the logical domain to the physical domain
- CEdge Define an edge of a given patch
- CEdgeCoordinatesTransformation Transform a coordinate from one edge to a coordinate on the other edge
- CElectrostaticalPotentialSimulation Base class for the advection field for the tests of the 2D polar advection operator
- CElectrostaticalPotentialSimulation_decentred_rotation Advection field for the tests of the 2D polar advection operator
- CElectrostaticalPotentialSimulation_rotation Advection field for the tests of the 2D polar advection operator
- CElectrostaticalPotentialSimulation_translation Advection field for the tests of the 2D polar advection operator
- CEuler A class which provides an implementation of an explicit Euler method
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- ►CEvaluator2D
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- ►CFemNonPeriodicQNSolver An operator which solves the Quasi-Neutrality equation using Finite Elements on a non-periodic domain
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- ►CFemPeriodicQNSolver An operator which solves the Quasi-Neutrality equation using Finite Elements on a periodic domain
- CFFTPoissonSolver
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- ►CFFTPoissonSolver< ddc::DiscreteDomain< DDims... >, FullDomain, ExecSpace, LayoutSpace > A class solve the follwing equation: \( -\Delta \phi = \rho \) using a Fourier transform
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- ►CFluidMoments A class that computes fluid moments of the distribution function
- Cfor_each_tuple_cat
- Cfor_each_tuple_cat< std::tuple< Tuples... >, Tuple >
- CFunctionToBeAdvected Base class for the test functions for the 2D polar advection operator
- CFunctionToBeAdvected_cos_4_elipse Test function for the 2D polar advection operator
- CFunctionToBeAdvected_gaussian Test function for the 2D polar advection operator
- CGaussLegendre
- CGaussLegendreCoefficients
- CGeometryXVx A class providing aliases for useful subdomains of the geometry
- CGeometryXYVxVy A class providing aliases for useful subdomains of the geometry
- CGridMu
- CGridTor1
- CGridTor2
- CGridTor3
- CGridVpar
- CHiddenNUBSplinesX
- CIAdvectionRP Define the base class of 2D advection operators in polar domain
- CIAdvectionSpatial A class which provides an advection operator
- CIAdvectionVelocity A class which provides an advection operator
- CIBoltzmannSolver An abstract class for solving a Boltzmann equation
- CIChargeDensityCalculator A class which calculates the charge density
- CIDimM
- CIDimP
- CIDimR
- CIDimSp
- CIDimVp
- CIDimVr
- CIDimVx
- CIDimVy
- CIDimX
- CIDimY
- CIEquilibrium An abstract class for initializing a distribution function that does not depend on space
- CIFluidInitialization An abstract class that allows for initializing a fluid species
- CIFluidSolver An abstract class for solving a fluid model
- CIFootFinder Define a base class for all the time integration methods used for the advection
- CIInitialization An abstract class that allows for initializing a distribution function
- CIInterpolator A class which provides an interpolating function
- CIInterpolatorRP A class which provides an interpolating function
- CInterface Represent a simple sticking of two edges
- Cinterpolator_on_domain
- Cinterpolator_on_domain< Interp, DDimI, ddc::DiscreteDomain< DDim... > > A structure which builds an interpolation type
- CIPoissonSolver
- CIPoissonSolver< ddc::DiscreteDomain< ODims... >, FullDomain, LayoutSpace, MemorySpace > An abstract class from which a Poisson solver can inherit
- CIPreallocatableInterpolator A class which provides access to an interpolating function which can be preallocated where useful
- CIPreallocatableInterpolatorRP A class which provides access to an interpolating function which can be preallocated where useful
- CIQNSolver Base class for a Quasi-Neutrality solver
- CIReactionRate An abstract interface representing a reaction rate that depends on temperature and density
- CIRightHandSide An abstract class representing a source in Boltzmann equation
- Cis_subdomain_collection
- Cis_subdomain_collection< DiscreteSubDomain< Tags... > >
- CITimeSolver An abstract class for solving a Boltzmann-Poisson system of equations
- CITimeSolverHybrid An abstract class for solving a Boltzmann-Poisson system of equations coupled to a fluid model
- CITimeSolverRP Base class for the time solvers
- CITimeStepper
- CIVlasovSolver
- CKineticSource A class that describes a source of particles
- CKrookSourceAdaptive A class that describes a source of particles
- CKrookSourceConstant A class that describes a source of particles
- CLagrange A class which implements Lagrange polynomials
- CLagrangeInterpolator A class for interpolating a function using Lagrange polynomials
- CManufacturedPoissonTest Defining the corresponding RHS of the Poisson equation for a given exact solution
- CMatrix
- CMatrix_Banded
- CMatrix_Center_Block
- CMatrix_Corner_Block
- CMatrix_Dense
- CMatrix_PDS_Tridiag
- CMatrix_Periodic_Banded
- CMatrixBatch MatrixBatch superclass for managing a collection of linear systems
- CMatrixBatchEll Matrix class which is able to manage and solve a batch of sparse linear systems
- CMatrixBatchTridiag A structure for solving a set of independant tridiagonal systems using a direct method
- CMaxwellianEquilibrium A class that initializes the distribution function as a Maxwellian
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- ►CMoments Moments discrete dimension to access constant attributes related to fluid moments
- CMu Define non periodic magnetic momentum \(\mu\)
- CNullAdvectionVelocity
- CNullFluidSolver A dommy class that solves a fluid model
- CNullQNSolver Null operator
- CPoissonLikeRHSFunction Type of right-hand side (rhs) function of the Poisson equation
- CPoissonSolution Base class for the exact solutions of the Poisson equation
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- ►CPolarBSplines A class containing all information describing polar bsplines
- CPolarBSplinesRP
- CPolarSpline A structure containing the two Chunks necessary to define a spline on a set of polar basis splines
- CPolarSplineEvaluator Define an evaluator on polar B-splines
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- ►CPolarSplineFEMPoissonLikeSolver Define a polar PDE solver for a Poisson-like equation
- CPolarSplineSpan A structure containing the two ChunkSpans necessary to define a reference to a spline on a set of polar basis splines
- CPolarSplineView A structure containing the two ChunkViews necessary to define a constant reference to a spline on a set of polar basis splines
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- ►CPolynomialEvaluator
- CPreallocatableLagrangeInterpolator A class which stores information necessary to create an instance of the LagrangeInterpolator class
- CPreallocatableSplineInterpolator A class which stores information necessary to create an instance of the SplineInterpolator class
- CPreallocatableSplineInterpolatorRP A class which stores information necessary to create a pointer to an instance of the SplineInterpolatorRP class
- CPredCorr A class that solves a Boltzmann-Poisson system of equations using a predictor-corrector scheme
- CPredCorrHybrid A class that solves a Boltzmann-Poisson system of equations coupled to a fluid particles model using a predictor-corrector scheme
- CQNSolver An operator which solves the Quasi-Neutrality equation using a fast Fourier transform
- CQuadrature A class providing an operator for integrating functions defined on a discrete domain
- CRDimP Define periodic real Theta dimension
- CRDimR Define non periodic real R dimension
- CRDimT A class which describes the real space in the temporal direction
- CRDimVp Define periodic real Theta velocity dimension
- CRDimVr Define non periodic real R velocity dimension
- CRDimVx Define non periodic real X velocity dimension
- CRDimVy Define non periodic real Y velocity dimension
- CRDimX Define non periodic real X dimension
- CRDimY Define non periodic real Y dimension
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- ►CRefinedDiscreteToCartesian A class for describing refined discrete 2D mappings from the logical domain to the physical domain
- CRestartInitialization A class that initializes the distribution function from a previous simulation
- CRK2 A class which provides an implementation of a second-order Runge-Kutta method
- CRK3 A class which provides an implementation of a third-order Runge-Kutta method
- CRK4 A class which provides an implementation of a fourth-order Runge-Kutta method
- CRotationAdvectionFieldSimulation Simulation of a rotated Gaussian
- CRotationSimulation Simulation of a rotated Gaussian
- CSingleModePerturbInitialization A class that initializes the distribution function as a perturbed Maxwellian
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- ►CSpeciesInformation Species discrete dimension to access constant attributes related to species
- CSplineFootFinder Define a base class for all the time integration methods used for the advection
- CSplineInterpolator A class for interpolating a function using splines
- CSplineInterpolatorRP A class for interpolating a function using splines in polar coordinates
- CSplitRightHandSideSolver A class that solves a Boltzmann equation using Strang's splitting
- CSplitVlasovSolver A class that solves a Vlasov equation using Strang's splitting
- Cto_tuple Transform a sequence S to a tuple:
- Cto_tuple< std::integer_sequence< T, Ints... > >
- Cto_tuple< std::pair< T, U > >
- CToDiscreteSubDomain A class to create a DiscreteSubDomain type from a TypeSeq
- CTor1 Define non periodic radial dimension \(r\)
- CTor2 Define periodic poloidal dimension \(\theta\)
- CTor3 Define periodic toroidal dimension \(\varphi\)
- CTranslationAdvectionFieldSimulation Simulation of a translated Gaussian
- CTranslationSimulation Simulation of a translated Gaussian
- Ctuple_to_types Transform a std::tuple<Args...> to a testing::Types<Args...>, identity otherwise
- Ctuple_to_types< std::tuple< Args... > >
- CVectorField Pre-declaration of VectorField
- CVectorFieldCommon
- CVectorFieldSpan Pre-declaration of VectorFieldSpan
- CVortexMergerDensitySolution Initial condition for the vortex merger simulation
- CVortexMergerEquilibria Equilibrium solution of a Vlasov-Poissson equations system in polar coordinates
+ CVpar Define non periodic parallel velocity \(v_\parallel\)
+ CBslAdvection1D A class which computes the advection along the dimension of interest IDimInterest
+ CBslAdvectionRP Define an advection operator on 2D \((r, \theta)\) domain
+ CBslAdvectionSpatial A class which computes the spatial advection along the dimension of interest DDimX
+ CBslAdvectionVelocity A class which computes the velocity advection along the dimension of interest DDimV
+ CBslExplicitPredCorrRP A second order explicit predictor-corrector for the Vlasov-Poisson equations
+ CBslImplicitPredCorrRP A second order implicit predictor-corrector for the Vlasov-Poisson equations
+ CBslPredCorrRP Predictor-corrector for the Vlasov-Poisson equations
+ CBSplinesP
+ CBSplinesR
+ CBSplinesVp
+ CBSplinesVr
+ CBSplinesVx
+ CBSplinesVy
+ CBSplinesX
+ CBSplinesY
+ CBumpontailEquilibrium A class that initializes the distribution function as a sum of two Maxwellian functions
+ Ccartesian_product_impl
+ Ccartesian_product_impl< std::tuple< std::tuple< HeadArgs... >, TailTuples... >, OutTupleOfTuples >
+ Ccartesian_product_impl< std::tuple<>, OutTupleOfTuples >
+ CCartesianSolution Define a Cartesian solution of the Poisson equation
+ CCartesianToBarycentricCoordinates
+ CChargeDensityCalculator A class which computes charges density with Kokkos
+ CCircularToCartesian A class for describing the circular 2D mapping
+ CCollisionsGuard Header Guard for collision operator
+ CCollisionsInter Class describing the inter-species collision operator
+
+
+ ►CCollisionsIntra Class describing the intra-species collision operator
+ CCollisionSpVparMu A class which computes the collision operator in (vpar,mu)
+ CConstantFluidInitialization A class that initializes a fluid species with constant moments
+ CConstantRate A class that describes a reaction rate that is constant
+
+ ►CCosineEvaluator
+ CCrankNicolson A class which provides an implementation of a Crank-Nicolson method
+ CCurvilinear2DToCartesian A class for describing curvilinear 2D mappings from the logical domain to the physical domain
+ CCurvilinearSolution Define a curvilinear solution of the Poisson equation
+ CCzarnyToCartesian A class for describing the Czarny 2D mapping
+ CDecentredRotationAdvectionFieldSimulation Simulation of a decentred rotated elipse-type function
+ CDecentredRotationSimulation Simulation of a decentred rotated elipse-type function
+ CDerivField
+ CDerivField< ElementType, ddc::DiscreteDomain< DDims... >, NDerivs, Allocator > A class which holds a chunk of memory describing a field and its derivatives
+ CDerivFieldCommon
+ CDerivFieldCommon< ChunkType, ddc::DiscreteDomain< DDims... > > An abstract class which holds a chunk of memory describing a field and its derivatives
+ CDerivFieldSpan
+ CDerivFieldSpan< ElementType, ddc::DiscreteDomain< DDims... >, LayoutStridedPolicy, MemorySpace > A class which holds references to chunks of memory describing a field and its derivatives
+ CDiffusiveNeutralSolver A class that solves a so-called "pressure-diffusive" fluid neutral model
+ CDimX_pC Tag the first non periodic dimension in the pseudo_Cartesian domain
+ CDimY_pC Tag the second non periodic dimension in the pseudo_Cartesian domain
+ CDiocotronDensitySolution The diocotron exact solution of the density \( \rho \)
+ CDiscreteSubDomain A class which describes a collection of ddc::DiscreteElements which form a subdomain
+ CDiscreteSubDomainIterator An iterator type for the DiscreteSubDomain
+ CDiscreteToCartesian A class for describing discrete 2D mappings from the logical domain to the physical domain
+ CEdge Define an edge of a given patch
+ CEdgeCoordinatesTransformation Transform a coordinate from one edge to a coordinate on the other edge
+ CElectrostaticalPotentialSimulation Base class for the advection field for the tests of the 2D polar advection operator
+ CElectrostaticalPotentialSimulation_decentred_rotation Advection field for the tests of the 2D polar advection operator
+ CElectrostaticalPotentialSimulation_rotation Advection field for the tests of the 2D polar advection operator
+ CElectrostaticalPotentialSimulation_translation Advection field for the tests of the 2D polar advection operator
+ CEuler A class which provides an implementation of an explicit Euler method
+
+ ►CEvaluator2D
+
+ ►CFemNonPeriodicQNSolver An operator which solves the Quasi-Neutrality equation using Finite Elements on a non-periodic domain
+
+ ►CFemPeriodicQNSolver An operator which solves the Quasi-Neutrality equation using Finite Elements on a periodic domain
+ CFFTPoissonSolver
+
+ ►CFFTPoissonSolver< ddc::DiscreteDomain< DDims... >, FullDomain, ExecSpace, LayoutSpace > A class solve the follwing equation: \( -\Delta \phi = \rho \) using a Fourier transform
+
+
+
+ ►CFluidMoments A class that computes fluid moments of the distribution function
+ Cfor_each_tuple_cat
+ Cfor_each_tuple_cat< std::tuple< Tuples... >, Tuple >
+ CFunctionToBeAdvected Base class for the test functions for the 2D polar advection operator
+ CFunctionToBeAdvected_cos_4_elipse Test function for the 2D polar advection operator
+ CFunctionToBeAdvected_gaussian Test function for the 2D polar advection operator
+ CGaussLegendre
+ CGaussLegendreCoefficients
+ CGeometryXVx A class providing aliases for useful subdomains of the geometry
+ CGeometryXYVxVy A class providing aliases for useful subdomains of the geometry
+ CGridMu
+ CGridTor1
+ CGridTor2
+ CGridTor3
+ CGridVpar
+ CHiddenNUBSplinesX
+ CIAdvectionRP Define the base class of 2D advection operators in polar domain
+ CIAdvectionSpatial A class which provides an advection operator
+ CIAdvectionVelocity A class which provides an advection operator
+ CIBoltzmannSolver An abstract class for solving a Boltzmann equation
+ CIChargeDensityCalculator A class which calculates the charge density
+ CIDimM
+ CIDimP
+ CIDimR
+ CIDimSp
+ CIDimVp
+ CIDimVr
+ CIDimVx
+ CIDimVy
+ CIDimX
+ CIDimY
+ CIEquilibrium An abstract class for initializing a distribution function that does not depend on space
+ CIFluidInitialization An abstract class that allows for initializing a fluid species
+ CIFluidSolver An abstract class for solving a fluid model
+ CIFootFinder Define a base class for all the time integration methods used for the advection
+ CIInitialization An abstract class that allows for initializing a distribution function
+ CIInterpolator A class which provides an interpolating function
+ CIInterpolatorRP A class which provides an interpolating function
+ CInterface Represent a simple sticking of two edges
+ Cinterpolator_on_domain
+ Cinterpolator_on_domain< Interp, DDimI, ddc::DiscreteDomain< DDim... > > A structure which builds an interpolation type
+ CIPoissonSolver
+ CIPoissonSolver< ddc::DiscreteDomain< ODims... >, FullDomain, LayoutSpace, MemorySpace > An abstract class from which a Poisson solver can inherit
+ CIPreallocatableInterpolator A class which provides access to an interpolating function which can be preallocated where useful
+ CIPreallocatableInterpolatorRP A class which provides access to an interpolating function which can be preallocated where useful
+ CIQNSolver Base class for a Quasi-Neutrality solver
+ CIReactionRate An abstract interface representing a reaction rate that depends on temperature and density
+ CIRightHandSide An abstract class representing a source in Boltzmann equation
+ Cis_subdomain_collection
+ Cis_subdomain_collection< DiscreteSubDomain< Tags... > >
+ CITimeSolver An abstract class for solving a Boltzmann-Poisson system of equations
+ CITimeSolverHybrid An abstract class for solving a Boltzmann-Poisson system of equations coupled to a fluid model
+ CITimeSolverRP Base class for the time solvers
+ CITimeStepper
+ CIVlasovSolver
+ CKineticSource A class that describes a source of particles
+ CKrookSourceAdaptive A class that describes a source of particles
+ CKrookSourceConstant A class that describes a source of particles
+ CLagrange A class which implements Lagrange polynomials
+ CLagrangeInterpolator A class for interpolating a function using Lagrange polynomials
+ CManufacturedPoissonTest Defining the corresponding RHS of the Poisson equation for a given exact solution
+ CMatrix
+ CMatrix_Banded
+ CMatrix_Center_Block
+ CMatrix_Corner_Block
+ CMatrix_Dense
+ CMatrix_PDS_Tridiag
+ CMatrix_Periodic_Banded
+ CMatrixBatch MatrixBatch superclass for managing a collection of linear systems
+ CMatrixBatchEll Matrix class which is able to manage and solve a batch of sparse linear systems
+ CMatrixBatchTridiag A structure for solving a set of independant tridiagonal systems using a direct method
+ CMaxwellianEquilibrium A class that initializes the distribution function as a Maxwellian
+
+ ►CMoments Moments discrete dimension to access constant attributes related to fluid moments
+ CMu Define non periodic magnetic momentum \(\mu\)
+ CNullAdvectionVelocity
+ CNullFluidSolver A dommy class that solves a fluid model
+ CNullQNSolver Null operator
+ CPoissonLikeRHSFunction Type of right-hand side (rhs) function of the Poisson equation
+ CPoissonSolution Base class for the exact solutions of the Poisson equation
+
+
+
+
+
+ ►CPolarBSplines A class containing all information describing polar bsplines
+ CPolarBSplinesRP
+ CPolarSpline A structure containing the two Chunks necessary to define a spline on a set of polar basis splines
+ CPolarSplineEvaluator Define an evaluator on polar B-splines
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+
+
+
+
+
+ ►CPolarSplineFEMPoissonLikeSolver Define a polar PDE solver for a Poisson-like equation
+ CPolarSplineSpan A structure containing the two ChunkSpans necessary to define a reference to a spline on a set of polar basis splines
+ CPolarSplineView A structure containing the two ChunkViews necessary to define a constant reference to a spline on a set of polar basis splines
+
+ ►CPolynomialEvaluator
+ CPreallocatableLagrangeInterpolator A class which stores information necessary to create an instance of the LagrangeInterpolator class
+ CPreallocatableSplineInterpolator A class which stores information necessary to create an instance of the SplineInterpolator class
+ CPreallocatableSplineInterpolatorRP A class which stores information necessary to create a pointer to an instance of the SplineInterpolatorRP class
+ CPredCorr A class that solves a Boltzmann-Poisson system of equations using a predictor-corrector scheme
+ CPredCorrHybrid A class that solves a Boltzmann-Poisson system of equations coupled to a fluid particles model using a predictor-corrector scheme
+ CQNSolver An operator which solves the Quasi-Neutrality equation using a fast Fourier transform
+ CQuadrature A class providing an operator for integrating functions defined on a discrete domain
+ CRDimP Define periodic real Theta dimension
+ CRDimR Define non periodic real R dimension
+ CRDimT A class which describes the real space in the temporal direction
+ CRDimVp Define periodic real Theta velocity dimension
+ CRDimVr Define non periodic real R velocity dimension
+ CRDimVx Define non periodic real X velocity dimension
+ CRDimVy Define non periodic real Y velocity dimension
+ CRDimX Define non periodic real X dimension
+ CRDimY Define non periodic real Y dimension
+
+
+
+
+
+
+
+
+ ►CRefinedDiscreteToCartesian A class for describing refined discrete 2D mappings from the logical domain to the physical domain
+ CRestartInitialization A class that initializes the distribution function from a previous simulation
+ CRK2 A class which provides an implementation of a second-order Runge-Kutta method
+ CRK3 A class which provides an implementation of a third-order Runge-Kutta method
+ CRK4 A class which provides an implementation of a fourth-order Runge-Kutta method
+ CRotationAdvectionFieldSimulation Simulation of a rotated Gaussian
+ CRotationSimulation Simulation of a rotated Gaussian
+ CSingleModePerturbInitialization A class that initializes the distribution function as a perturbed Maxwellian
+
+ ►CSpeciesInformation Species discrete dimension to access constant attributes related to species
+ CSplineFootFinder Define a base class for all the time integration methods used for the advection
+ CSplineInterpolator A class for interpolating a function using splines
+ CSplineInterpolatorRP A class for interpolating a function using splines in polar coordinates
+ CSplitRightHandSideSolver A class that solves a Boltzmann equation using Strang's splitting
+ CSplitVlasovSolver A class that solves a Vlasov equation using Strang's splitting
+ Cto_tuple Transform a sequence S to a tuple:
+ Cto_tuple< std::integer_sequence< T, Ints... > >
+ Cto_tuple< std::pair< T, U > >
+ CToDiscreteSubDomain A class to create a DiscreteSubDomain type from a TypeSeq
+ CTor1 Define non periodic radial dimension \(r\)
+ CTor2 Define periodic poloidal dimension \(\theta\)
+ CTor3 Define periodic toroidal dimension \(\varphi\)
+ CTranslationAdvectionFieldSimulation Simulation of a translated Gaussian
+ CTranslationSimulation Simulation of a translated Gaussian
+ Ctuple_to_types Transform a std::tuple<Args...> to a testing::Types<Args...>, identity otherwise
+ Ctuple_to_types< std::tuple< Args... > >
+ CVectorField Pre-declaration of VectorField
+ CVectorFieldCommon
+ CVectorFieldSpan Pre-declaration of VectorFieldSpan
+ CVortexMergerDensitySolution Initial condition for the vortex merger simulation
+ CVortexMergerEquilibria Equilibrium solution of a Vlasov-Poissson equations system in polar coordinates
diff --git a/annotated.js b/annotated.js
index 692d5d1f9..914432d3a 100644
--- a/annotated.js
+++ b/annotated.js
@@ -12,6 +12,7 @@ var annotated =
[ "AdvectionSimulation", "classAdvectionSimulation.html", "classAdvectionSimulation" ],
[ "AnalyticalInvertibleCurvilinear2DToCartesian", "classAnalyticalInvertibleCurvilinear2DToCartesian.html", "classAnalyticalInvertibleCurvilinear2DToCartesian" ],
[ "BernsteinPolynomialBasis", "classBernsteinPolynomialBasis.html", "classBernsteinPolynomialBasis" ],
+ [ "BslAdvection1D", "classBslAdvection1D.html", "classBslAdvection1D" ],
[ "BslAdvectionRP", "classBslAdvectionRP.html", "classBslAdvectionRP" ],
[ "BslAdvectionSpatial", "classBslAdvectionSpatial.html", "classBslAdvectionSpatial" ],
[ "BslAdvectionVelocity", "classBslAdvectionVelocity.html", "classBslAdvectionVelocity" ],
diff --git a/bsl__advection__1d_8hpp_source.html b/bsl__advection__1d_8hpp_source.html
new file mode 100644
index 000000000..93ed6c2a1
--- /dev/null
+++ b/bsl__advection__1d_8hpp_source.html
@@ -0,0 +1,309 @@
+
+
+
+
+
+
+
+ CVpar Define non periodic parallel velocity \(v_\parallel\)
+
+ BslAdvection1D(FunctionPreallocatableInterpolatorType const &function_interpolator, AdvectionFieldBuilder const &adv_field_builder, AdvectionFieldEvaluator const &adv_field_evaluator, TimeStepper const &time_stepper) BslAdvection1D< IDimInterest, AdvectionDomain, FunctionDomain, AdvectionFieldBuilder, AdvectionFieldEvaluator, TimeStepper > inlineexplicit
+ operator()(FunctionSpan const allfdistribu, AdvecFieldSpan const advection_field, double const dt, std::optional< AdvecFieldDerivView > const advection_field_derivatives_min=std::nullopt, std::optional< AdvecFieldDerivView > const advection_field_derivatives_max=std::nullopt) const BslAdvection1D< IDimInterest, AdvectionDomain, FunctionDomain, AdvectionFieldBuilder, AdvectionFieldEvaluator, TimeStepper > inline
+~BslAdvection1D()=default (defined in BslAdvection1D< IDimInterest, AdvectionDomain, FunctionDomain, AdvectionFieldBuilder, AdvectionFieldEvaluator, TimeStepper >) BslAdvection1D< IDimInterest, AdvectionDomain, FunctionDomain, AdvectionFieldBuilder, AdvectionFieldEvaluator, TimeStepper >
+
+
+
+Public Member Functions
+ BslAdvection1D (FunctionPreallocatableInterpolatorType const &function_interpolator, AdvectionFieldBuilder const &adv_field_builder, AdvectionFieldEvaluator const &adv_field_evaluator, TimeStepper const &time_stepper)
+ Constructor when the advection domain and the function domain are different. More...
+
+FunctionSpan operator() (FunctionSpan const allfdistribu, AdvecFieldSpan const advection_field, double const dt, std::optional< AdvecFieldDerivView > const advection_field_derivatives_min=std::nullopt, std::optional< AdvecFieldDerivView > const advection_field_derivatives_max=std::nullopt) const
+ Advects allfdistribu along the advection dimension IDimInterest for a duration dt. More...
+ Detailed Description
+template<class IDimInterest, class AdvectionDomain, class FunctionDomain, class AdvectionFieldBuilder, class AdvectionFieldEvaluator, class TimeStepper = Euler<device_t<ddc::Chunk< ddc::Coordinate<typename IDimInterest::continuous_dimension_type>, AdvectionDomain>>, device_t<ddc::Chunk<double, AdvectionDomain>>>>
+
+
+class BslAdvection1D< IDimInterest, AdvectionDomain, FunctionDomain, AdvectionFieldBuilder, AdvectionFieldEvaluator, TimeStepper >
+
+
+
+
+
+ IDimInterest The dimension along which the advection is computed. It refers to the dimension of \( x_i \) in the equation.
+ AdvectionDomain The domain \( \Omega' \) where the characteristic equation is solved. It also refers to the domain of the advection field. It had to also be defined on the IDimInterest for the time integration method.
+ FunctionDomain The domain \( \Omega \) where allfdistribu is defined.
+ AdvectionFieldBuilder The type of the spline builder for the advection field (see SplineBuilder).
+ AdvectionFieldEvaluator The type of the spline evalutor for the advection field (see SplineEvaluator).
+
+ TimeStepper The time integration method applied to solve the characteristic equation. The method is picked among the child classes of ITimeStepper. Constructor & Destructor Documentation
+
+◆ BslAdvection1D()
+
+
+
+
+
+
+
+
+
+
+
+ BslAdvection1D< IDimInterest, AdvectionDomain, FunctionDomain, AdvectionFieldBuilder, AdvectionFieldEvaluator, TimeStepper >::BslAdvection1D
+ (
+ FunctionPreallocatableInterpolatorType const &
+ function_interpolator,
+
+
+
+
+ AdvectionFieldBuilder const &
+ adv_field_builder,
+
+
+
+
+ AdvectionFieldEvaluator const &
+ adv_field_evaluator,
+
+
+
+
+ TimeStepper const &
+ time_stepper
+
+
+
+ )
+
+
+inlineexplicit
+
+
+
+
+
+ [in] function_interpolator interpolator along the IDimInterest direction to interpolate the advected function (allfdistribu) on the domain of the function.
+ [in] adv_field_builder builder along the IDimInterest direction to build a spline representation of the advection field on the function domain.
+ [in] adv_field_evaluator evaluator along the IDimInterest direction to evaluate the advection field spline representation on the function domain.
+
+ [in] time_stepper time integration method for the characteristic equation. Member Function Documentation
+
+◆ operator()()
+
+
+
+
+
+
+
+
+
+
+
+ FunctionSpan BslAdvection1D< IDimInterest, AdvectionDomain, FunctionDomain, AdvectionFieldBuilder, AdvectionFieldEvaluator, TimeStepper >::operator()
+ (
+ FunctionSpan const
+ allfdistribu,
+
+
+
+
+ AdvecFieldSpan const
+ advection_field,
+
+
+
+
+ double const
+ dt,
+
+
+
+
+ std::optional< AdvecFieldDerivView > const
+ advection_field_derivatives_min =
+ std::nullopt
,
+
+
+
+ std::optional< AdvecFieldDerivView > const
+ advection_field_derivatives_max =
+ std::nullopt
+
+
+ )
+ const
+
+inline
+
+
+
+
+ [in,out] allfdistribu Reference to the advected function, allocated on the device
+ [in] advection_field Reference to the advection field, allocated on the device.
+ [in] advection_field_derivatives_min Reference to the advection field derivatives at the left side of the interest dimension, allocated on the device.
+ [in] advection_field_derivatives_max Reference to the advection field derivatives at the right side of the interest dimension, allocated on the device.
+ [in] dt Time step.
+
+
The documentation for this class was generated from the following file:
+
+
diff --git a/navtreedata.js b/navtreedata.js
index fb22fa3cc..44d31819f 100644
--- a/navtreedata.js
+++ b/navtreedata.js
@@ -69,14 +69,14 @@ var NAVTREE =
[ "Functions used for input and output.", "src_io.html", null ],
[ "Tests", "tests.html", "tests" ],
[ "Script to automise :", "tests_geometry5D_collisions.html", [
- [ "- the creation of the initial restart file with the python script init_distribution.py", "tests_geometry5D_collisions.html#autotoc_md56", null ],
- [ "- the creation of the input YAML file required as input of the C++ simulation testcollision", "tests_geometry5D_collisions.html#autotoc_md57", null ],
- [ "For instance, the following command", "tests_geometry5D_collisions.html#autotoc_md58", null ],
- [ "create the folder D_INPUT_PARAMS_ION_1X1X1X128X64.YAML containing:", "tests_geometry5D_collisions.html#autotoc_md59", null ],
- [ "- GysX_rst_00000.h5 : output of the python script init_distribution.py", "tests_geometry5D_collisions.html#autotoc_md60", null ],
- [ "- GysX_rst_00001.h5 : output of the C++ collision executable", "tests_geometry5D_collisions.html#autotoc_md61", null ],
- [ "- coll_ref.yml : input for C++ collision executable automatically created by the bash script testcollision.sh", "tests_geometry5D_collisions.html#autotoc_md62", null ],
- [ "- diff_f_vpar_mu_itor1eq0_itor2eq0_itor3eq0_ispeq0.png : output figure to compare the results between GysX_rst_00000.h5 and GysX_rst_00001.h5", "tests_geometry5D_collisions.html#autotoc_md63", null ]
+ [ "- the creation of the initial restart file with the python script init_distribution.py", "tests_geometry5D_collisions.html#autotoc_md62", null ],
+ [ "- the creation of the input YAML file required as input of the C++ simulation testcollision", "tests_geometry5D_collisions.html#autotoc_md63", null ],
+ [ "For instance, the following command", "tests_geometry5D_collisions.html#autotoc_md64", null ],
+ [ "create the folder D_INPUT_PARAMS_ION_1X1X1X128X64.YAML containing:", "tests_geometry5D_collisions.html#autotoc_md65", null ],
+ [ "- GysX_rst_00000.h5 : output of the python script init_distribution.py", "tests_geometry5D_collisions.html#autotoc_md66", null ],
+ [ "- GysX_rst_00001.h5 : output of the C++ collision executable", "tests_geometry5D_collisions.html#autotoc_md67", null ],
+ [ "- coll_ref.yml : input for C++ collision executable automatically created by the bash script testcollision.sh", "tests_geometry5D_collisions.html#autotoc_md68", null ],
+ [ "- diff_f_vpar_mu_itor1eq0_itor2eq0_itor3eq0_ispeq0.png : output figure to compare the results between GysX_rst_00000.h5 and GysX_rst_00001.h5", "tests_geometry5D_collisions.html#autotoc_md69", null ]
] ],
[ "Selalib++", "vendor_sll.html", "vendor_sll" ],
[ "API reference", "annotated.html", "annotated" ],
@@ -87,12 +87,12 @@ var NAVTREE =
var NAVTREEINDEX =
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-"structIDimM.html"
+"classCrankNicolson.html",
+"classFFTPoissonSolver_3_01ddc_1_1DiscreteDomain_3_01DDims_8_8_8_01_4_00_01FullDomain_00_01ExecSpace_00_01LayoutSpace_01_4.html#ad5e9a864bbb0dd8dc764e4a5edc746bf",
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+"geometry__pseudo__cartesian_8hpp_source.html",
+"structFemPeriodicQNSolver_1_1QMeshX.html"
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var SYNCONMSG = 'click to disable panel synchronisation';
diff --git a/navtreeindex0.js b/navtreeindex0.js
index 02ad8d348..a9927e435 100644
--- a/navtreeindex0.js
+++ b/navtreeindex0.js
@@ -14,9 +14,10 @@ var NAVTREEINDEX0 =
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"barycentric__coordinates_8hpp_source.html":[19,2,0,0,0,0,1],
"bernstein_8hpp_source.html":[19,2,0,0,0,1],
+"bsl__advection__1d_8hpp_source.html":[19,0,0,0],
"bsl__advection__rp_8hpp_source.html":[19,0,4,0,1],
-"bsl__advection__vx_8hpp_source.html":[19,0,0,0],
-"bsl__advection__x_8hpp_source.html":[19,0,0,1],
+"bsl__advection__vx_8hpp_source.html":[19,0,0,1],
+"bsl__advection__x_8hpp_source.html":[19,0,0,2],
"bsl__predcorr_8hpp_source.html":[19,0,4,6,0],
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"bsl__predcorr__second__order__implicit_8hpp_source.html":[19,0,4,6,2],
@@ -106,148 +107,147 @@ var NAVTREEINDEX0 =
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index e3c4acd25..40f60bb39 100644
--- a/pages.html
+++ b/pages.html
@@ -155,13 +155,14 @@
▼ src
- ▼ advection
- bsl_advection_vx.hpp
- bsl_advection_x.hpp
- iadvectionvx.hpp
- iadvectionx.hpp
- nulladvectionvx.hpp
- ▼ collision
- CollisionSpVparMu.hpp
- koliop_interface.hpp
- ▼ data_types
- deriv_details.hpp
- derivative_field.hpp
- derivative_field_common.hpp
- derivative_field_span.hpp
- discrete_subdomain.hpp
- vector_field.hpp
- vector_field_common.hpp
- vector_field_span.hpp
- ▼ geometry5D
-
- ► geometry
- ▼ geometryRTheta
-
-
-
-
-
-
- ► advection
-
- ► advection_field
-
- ► geometry
-
-
-
- ► initialization
-
-
- ► interpolation
-
-
-
- ► poisson
-
-
-
-
- ► time_solver
- ▼ geometryXVx
-
-
-
- ► boltzmann
-
- ► geometry
-
-
-
-
-
-
-
-
-
-
- ► geometryMX
-
-
-
-
-
-
- ► initialization
-
-
-
-
-
-
-
- ► poisson
-
-
-
-
-
-
-
-
- ► rhs
-
-
- ► time_integration
-
-
- ► time_integration_hybrid
-
- ► utils
- ▼ geometryXYVxVy
-
- ► geometry
-
-
-
-
- ► initialization
-
-
-
-
-
- ► poisson
-
-
- ► time_integration
-
-
- ► vlasov
- ▼ interpolation
- iinterpolator.hpp
- Lagrange.hpp
- Lagrange_interpolator.hpp
- spline_interpolator.hpp
- ▼ io
- input.hpp
- output.hpp
- ▼ multipatch
-
-
-
- ► interfaces
- ▼ paraconfpp
- paraconfpp.hpp
- ▼ pde_solvers
- fft_poisson_solver.hpp
- ipoisson_solver.hpp
- ▼ quadrature
- compute_norms.hpp File providing the L1 and the L2 norms
- neumann_spline_quadrature.hpp File providing quadrature coefficients via a spline quadrature
- quadrature.hpp
- quadrature_coeffs_nd.hpp File providing helper functions for defining multi-dimensional quadrature methods
- simpson_quadrature.hpp
- spline_quadrature.hpp File providing quadrature coefficients via a spline quadrature
- trapezoid_quadrature.hpp File providing quadrature coefficients via the trapezoidal method
- ▼ speciesinfo
- moments.hpp
- species_info.hpp
- species_init.hpp
- ▼ timestepper
- crank_nicolson.hpp
- euler.hpp
- itimestepper.hpp
- rk2.hpp
- rk3.hpp
- rk4.hpp
- ▼ utils
- assert.hpp
- ddc_helper.hpp
- directional_tag.hpp
- preprocessor.hpp
- transpose.hpp
- utils_tools.hpp File Describing useful functions
- ▼ tests
- ▼ geometryRTheta
-
- ► 2d_spline_interpolator
-
-
-
- ► advection_2d_rp
-
- ► advection_field_rp
-
-
- ► polar_poisson
- ▼ vendor
- ▼ sll
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
- ► include
-
-
-
-
+ ► tests
+ bsl_advection_1d.hpp
+ bsl_advection_vx.hpp
+ bsl_advection_x.hpp
+ iadvectionvx.hpp
+ iadvectionx.hpp
+ nulladvectionvx.hpp
+ ▼ collision
+ CollisionSpVparMu.hpp
+ koliop_interface.hpp
+ ▼ data_types
+ deriv_details.hpp
+ derivative_field.hpp
+ derivative_field_common.hpp
+ derivative_field_span.hpp
+ discrete_subdomain.hpp
+ vector_field.hpp
+ vector_field_common.hpp
+ vector_field_span.hpp
+ ▼ geometry5D
+
+ ► geometry
+ ▼ geometryRTheta
+
+
+
+
+
+
+ ► advection
+
+ ► advection_field
+
+ ► geometry
+
+
+
+ ► initialization
+
+
+ ► interpolation
+
+
+
+ ► poisson
+
+
+
+
+ ► time_solver
+ ▼ geometryXVx
+
+
+
+ ► boltzmann
+
+ ► geometry
+
+
+
+
+
+
+
+
+
+
+ ► geometryMX
+
+
+
+
+
+
+ ► initialization
+
+
+
+
+
+
+
+ ► poisson
+
+
+
+
+
+
+
+
+ ► rhs
+
+
+ ► time_integration
+
+
+ ► time_integration_hybrid
+
+ ► utils
+ ▼ geometryXYVxVy
+
+ ► geometry
+
+
+
+
+ ► initialization
+
+
+
+
+
+ ► poisson
+
+
+ ► time_integration
+
+
+ ► vlasov
+ ▼ interpolation
+ iinterpolator.hpp
+ Lagrange.hpp
+ Lagrange_interpolator.hpp
+ spline_interpolator.hpp
+ ▼ io
+ input.hpp
+ output.hpp
+ ▼ multipatch
+
+
+
+ ► interfaces
+ ▼ paraconfpp
+ paraconfpp.hpp
+ ▼ pde_solvers
+ fft_poisson_solver.hpp
+ ipoisson_solver.hpp
+ ▼ quadrature
+ compute_norms.hpp File providing the L1 and the L2 norms
+ neumann_spline_quadrature.hpp File providing quadrature coefficients via a spline quadrature
+ quadrature.hpp
+ quadrature_coeffs_nd.hpp File providing helper functions for defining multi-dimensional quadrature methods
+ simpson_quadrature.hpp
+ spline_quadrature.hpp File providing quadrature coefficients via a spline quadrature
+ trapezoid_quadrature.hpp File providing quadrature coefficients via the trapezoidal method
+ ▼ speciesinfo
+ moments.hpp
+ species_info.hpp
+ species_init.hpp
+ ▼ timestepper
+ crank_nicolson.hpp
+ euler.hpp
+ itimestepper.hpp
+ rk2.hpp
+ rk3.hpp
+ rk4.hpp
+ ▼ utils
+ assert.hpp
+ ddc_helper.hpp
+ directional_tag.hpp
+ preprocessor.hpp
+ transpose.hpp
+ utils_tools.hpp File Describing useful functions
+ ▼ tests
+ ▼ geometryRTheta
+
+ ► 2d_spline_interpolator
+
+
+
+ ► advection_2d_rp
+
+ ► advection_field_rp
+
+
+ ► polar_poisson
+ ▼ vendor
+ ▼ sll
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+ ► include
+
+
+
+
► tests Time integration hybrid Functions used for input and output.
- ▼Tests
- ▼Tests : Geometry (r, theta)
- Tests on the 2D polar advection operator
- Tests on spline interpolator in polar coordinates
- Tests on the 2D polar poisson solver
- Script to automise :
- ▼Selalib++
+ Mappings
+ Tests on the templated advection operators
+ ▼Tests : Geometry (r, theta)
+ Tests on the 2D polar advection operator
+ Tests on spline interpolator in polar coordinates
+ Tests on the 2D polar poisson solver
+ Script to automise :
+ ▼Selalib++
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index 9f58898be..41310e1c3 100644
--- a/search/all_1.js
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index 5b806d27c..3ac6284f9 100644
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index a42698fef..fc585f84a 100644
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diff --git a/src.js b/src.js
index e98186cd2..a0dbc83a8 100644
--- a/src.js
+++ b/src.js
@@ -2,7 +2,8 @@ var src =
[
[ "Advection methods", "src_advection.html", [
[ "Spatial advection", "src_advection.html#src_advection__Spatial_advection", null ],
- [ "Velocity advection", "src_advection.html#src_advection__Velocity_advection", null ]
+ [ "Velocity advection", "src_advection.html#src_advection__Velocity_advection", null ],
+ [ "1D advection with a given advection field", "src_advection.html#src_advection__1D_advection_with_a_given_advection_field", null ]
] ],
[ "Geometry (r, theta)", "src_geometryRTheta.html", "src_geometryRTheta" ],
[ "Geometry (x, v_x)", "src_geometryXVx.html", "src_geometryXVx" ],
diff --git a/src_advection.html b/src_advection.html
index c0c112ccb..3abeda8c2 100644
--- a/src_advection.html
+++ b/src_advection.html
@@ -117,7 +117,72 @@ Mappings
+1D advection with a given advection field
+
+
+
+
+Example of use
+
+
+
+Parameters
+
+
+tests/advection/
folder).
+
Explicit Euler method
-
+
Crank-Nicolson method
-
+
RK3 method
-
+
RK4 method
@@ -238,7 +238,7 @@
\[\det(J) det(D_{G}^{-1}) (J^{-1})^{T} D_G = \begin{bmatrix} \frac{j_{22}}{\sqrt{g_{22}}} & - \frac{j_{21}}{\sqrt{g_{11}}} \\ - \frac{j_{12}}{\sqrt{g_{22}}} & \frac{j_{11}}{\sqrt{g_{11}}} \end{bmatrix}, \]
to get the advection field along the physical domain axis.
-The test of the advection operator are implemented in the tests/geometryRTheta/advection_2d_rp/
folder (Tests on the 2D polar advection operator).
It tests:
The tests of the convergence order are made for constant CFL which means it checks the slope of the errors (infinity norm of the difference at the final time)
for \((N_r\times N_\theta, dt) = (N_{r,0}\times N_{\theta,0}, dt_0)\) and then \((n*N_{r,0}\times n*N_{\theta,0}, dt_0/n)\) for \(n = 1, 2, 4, 8, ...\).
[1] Edoardo Zoni, Yaman Güçlü. "Solving hyperbolic-elliptic problems on singular mapped disk-like domains with the method of characteristics and spline finite elements". (https://doi.org/10.1016/j.jcp.2019.108889.) Journal of Computational Physics (2019).
-This folder contains:
Once the advection field computed, it is given as input to the BslAdvectionRP operator to advect the density \(\rho\) function. The BslAdvectionRP operator can handle the advection with an advection field along \((x,y)\) and with an advection field along \((r,\theta)\). But as the BslAdvectionRP operator advects in the physical domain, it is recommend to work with the advection field along \((x,y)\).
-Thanks to the spline representation, the derivatives \(\partial_r \phi\) and \(\partial_\theta \phi\) are computed. The computation of the electrical field can be ill-defined around the O-point so we treat this area separately.
(In the code, we chose \(\theta_1 = \frac{\pi}{4}\) and \(\theta_2 = - \frac{\pi}{4}\), and \(\varepsilon = 10^{-12}\).)
Firstly, the derivatives \(\partial_r \phi\) and \(\partial_\theta \phi\) are also computed here.
-In general coordinates system, the gradiant of a function is given by
@@ -184,7 +184,7 @@with \(\nabla_{y_1, y_2} f = [\partial_{y_1} f, \partial_{y_2} f]^T\) and \(\nabla_{x_1, x_2} f = \sum_i \sum_j \partial_{x_i} f g^{ij} \sqrt{g_{jj}} \hat{e}_j\).
-@@ -199,11 +199,11 @@
In the code, the O-point is differently treated. The domain is splitted between a domain without the O-point ( \((0,\theta), \forall \theta\)) and the domain containing only the O-point. For the first domain, we compute the advection field along the logical axis as explain previously. On the second domain, we compute the unique value of the advection field along the physical axis using the linearisation done in the Advection field along the physical domain axis section.
-[1] Edoardo Zoni, Yaman Güçlü, "Solving hyperbolic-elliptic problems on singular mapped disk-like domains with the method of characteristics and spline finite elements", https://doi.org/10.1016/j.jcp.2019.108889, Journal of Computational Physics, 2019.
-The initializatrion and equilibrium fonctions are defined in the DiocotronDensitySolution class.
-We suppose as perturbed initial condition
with \(p = 50\), \(\bar{r} = \frac{R_1 + R_2}{2}\) and \(d = \frac{R_2 - R_1}{2}\). This last version is implemented in the code.
-The associated equilibrium is
or
The DiocotronDensitySolution also solves the dispersion relation:
@@ -144,7 +144,7 @@
More details about the diocotron simulation are given in Vortex merger.
-The equilibrium is determined by the eigenvalue problem of finding \((\sigma, \phi)\) such that
@@ -162,7 +162,7 @@
Then, we repeat all the steps until \(|\sigma^i - \sigma^{i-1}| \leq \tau\) for a given tolerance.
For the vortex merger simulation, we choose \(f(\phi)= \phi^2\) and \(\phi_{\text{max}} = 1\).
-[1] Edoardo Zoni, Yaman Güçlü, "Solving hyperbolic-elliptic problems on singular mapped disk-like domains with the method of characteristics and spline finite elements", https://doi.org/10.1016/j.jcp.2019.108889, Journal of Computational Physics, 2019.
diff --git a/src_geometryRTheta_poisson.html b/src_geometryRTheta_poisson.html index eef7e817f..e3812a869 100644 --- a/src_geometryRTheta_poisson.html +++ b/src_geometryRTheta_poisson.html @@ -113,21 +113,21 @@with the boundary condition \(\phi = 0\), on \(\partial \Omega\).
To solve this equation, the PolarSplineFEMPoissonLikeSolver uses a finite element method on the B-splines.
-We introduce a basis of B-splines \(\{B_l\}_l\), cross-product of two 1D B-splines basis:
\[\{B_l\}_l = \{b_{i,r} b_{j,\theta}\}_{i n_{n,\theta} +j}. \]
-To conserve \(\mathcal{C}^k\) property at the O-point, the B-splines basis is modified.
The \(\frac{(k+1)(k+2)}{2}\) first elements in the 1D B-splines basis in the \(r\) dimension are removed, and replaced by 3 functions, linear combinations of these removed B-splines. (See (2.34) in Emily Bourne's thesis.)
The linear composition uses as coefficients, the Berstein polynomials defined from barycentric coordinates.
The B-splines with the treatment of the O-point, are called PolarBSplines and are written \(\{\hat{B}_l\}_l\).
-The Poisson-like equation is solved by solving its weak form:
diff --git a/src_multipatch_interfaces.html b/src_multipatch_interfaces.html index bd95d6a97..7694ab491 100644 --- a/src_multipatch_interfaces.html +++ b/src_multipatch_interfaces.html @@ -108,7 +108,7 @@
We follow the idea to represent the topology of a multipatch domain using the idea of domain manifolds (see [1]). This means that we have several independent tensor-product logical domains and define their sticking via coordinate transformations.
Remark: In the referenced paper, the authors use affine isometries of the entire patch instead of coordinate transformations of the faces. This is equivalent to our approach in the sense that, when the scaling of the domains is removed and we consider only unit squares as logical domains, the coordinate transformations of the faces and the information about which edges are identified determine the isometries used in the paper and vice versa. This is easy to show.
-For simplicity, we will constrain ourselves to the 2D case, but this approach could be generalized to arbitrary dimensions.
Let \(\Omega\) be the domain of interest and assume that we have patches \(\Omega^{(i)}\), \(i=1,...,K\), which are disjoint, s.t.
@@ -118,13 +118,13 @@
where the rectangular domain \([a_x^{(i)}, b_x^{(i)}]\times[a_y^{(i)} b_y^{(i)}]\) defines the logical coordinates for the patch. We call this logical coordinate domain the logical patch.
-So we obtain four logical edges
\[ [a_x^{(i)}, b_x^{(i)}] \times \{ a_y^{(i)} \}, \quad [a_x^{(i)}, b_x^{(i)}] \times \{ b_y^{(i)} \}, \quad \{ a_x^{(i)} \} \times [a_y^{(i)}, b_y^{(i)}], \quad \{ b_x^{(i)} \} \times [a_y^{(i)}, b_y^{(i)}] \]
In the code, we define edges as follows. Every edge of a logical patch is identified via the patch it belongs to, the dimension and whether it is at the front or the back of the domain. So e.g. the edge \([a_x^{(i)}, b_x^{(i)}] \times \{ a_y^{(i)} \}\) would be identified with patch \(i\), dimensions RDimXi
and FRONT
. \([a_x^{(i)}, b_x^{(i)}] \times \{ b_y^{(i)} \}\) would be identified with patch \(i\), dimensions RDimXi
and BACK
and \(\{ b_x^{(i)} \} \times [a_y^{(i)}, b_y^{(i)}]\) would be identified with patch \(i\), dimensions RDimYi
and BACK
.
Any edge can then be identified with an edge on another patch. This corresponds to the 'sticking'. So for a different patch \(\Omega^{(j)}\), we have the logical coordinate domain \([a_x^{(j)}, b_x^{(j)}] \times [a_y^{(j)} b_y^{(j)}]\). If we want to stick patch \(i\) to patch \(j\), we have to determine the edges that are identified and how they are identified. The way that they are identified is mathematically determined via the coordinate transformation from one edge to the other. Since the transformations are supposed to be affine and bijective, there are only two options: The transformation can be order preserving or order reversing (this corresponds to the orientation of the phyiscal edge where two parametrizations coming from the two patches can have either the same or the opposite orientation respectively).
So for example, we want to stick the edge \(\{ a_x^{(i)} \} \times [a_y^{(i)}, b_y^{(i)}]\) on patch \(i\) to the edge \([a_x^{(j)}, b_x^{(j)}] \times \{ b_y^{(j)} \}\) on patch \(j\). If the transformation is order-preserving (i.e. the orientations of the parametrizations of the physical edge agree), then the transformation from the first edge to the second is
diff --git a/tests.html b/tests.html index fa8c5c375..741946920 100644 --- a/tests.html +++ b/tests.html @@ -105,6 +105,7 @@
The tests
folder contains the tests of the different elements implemented in the src
folder. It is broken up into the following sub-folders:
The test is the following:
+\[ \partial_t f(t,x) + A(x) \partial_x f(t,x) = 0, \] +
+on \(\Omega = [-\pi, \pi]\) with
++\[\left\{ \begin{aligned} & f_0(x) = \sin(2x), \\ & A(x) = \sin(x). \end{aligned} \right. \] +
+We test it on a grid \(N_x = 32\) with \(dt = 0.05\). The simulation runs on \(t\in[0,0.4]\) and the relative error is expected to be below \( 5*10^{-3}\).
+The test is the following:
+\[ \partial_t f(t,x, v_x) + v_x \partial_x f(t,x, v_x) = 0, \\ \] +
+on \(\Omega = [-\pi, \pi]\times[-6, 6]\) with
++\[\left\{ \begin{aligned} & f_0(x, v_x) = \cos(x), \\ & A(x, v_x) = v_x. \end{aligned} \right. \] +
+We test it on a grid \(N_x\times N_{v_x} = 100\times50\) with \(dt = 0.1\). The simulation runs on \(t\in[0,0.4]\) and the relative error is expected to be below \( 5*10^{-7}\).
+The test is the following:
+\[ \partial_t f(t,x,y,v_x, v_y) + A(x,y) \cdot \nabla f(t,x,y, v_x, v_y) = 0, \] +
+on \(\Omega = [-0.5, 0.5]^2\times\{0,1\}^2\) with
++\[\left\{ \begin{aligned} & f_0(x) = \frac{1}{2}(G(r_1(x,y)) + G(r_2(x,y))), \\ & A(x, y) = \frac{1}{2\pi} \begin{bmatrix} \sin(2\pi x) \\ \sin(2\pi y) \\ \end{bmatrix}, \end{aligned} \right. \] +
+with
++\[\left\{ \begin{aligned} & G (r) = \cos(\frac{\pi r}{2a}) * \mathbb{1}_{r<a}(r), \\ & r_1 (x,y) = \sqrt{x^2 + 8 y^2}, \\ & r_2 (x,y) = \sqrt{8 x^2 + y^2}, \\ & \omega = 2 \pi, \\ & (x_c, y_c) = (0.25, 0). \\ \end{aligned} \right. \] +
+We test it on a grid \(N_x \times N_y \times N_{v_x} \times N_{v_y} = 60 \times 60 \times 2 \times 2\) with \(dt = 0.05\). The simulation runs on \(t\in[0,0.2]\) and the relative error is expected to be below \( 7*10^{-2}\).
+tests/geometryXVx/spatialadvection.cpp
which tests the BslAdvectionSpatial operator.The test is the following:
+\[ \partial_t f_s(t,x, v_x) - \sqrt{\frac{m_e}{m_s}} v_x \partial_x f_s(t,x, v_x) = 0, \\ \] +
+on \(\Omega = [-\pi, \pi]\times[-6, 6]\) with
++\[\left\{ \begin{aligned} & f_0(x, v_x) = \cos(x), \\ & A(x, v_x) = - \sqrt{\frac{m_e}{m_s}} v_x. \end{aligned} \right. \] +
+We test it on a grid \(N_x\times N_{v_x} = 100\times50\) with \(dt = 0.1\). The simulation runs on \(t\in[0,0.1]\) and the relative error is expected to be below \( 1*10^{-6}\).
+tests/geometryXVx/velocityadvection.cpp
which tests the BslAdvectionVelocity operator.The test is the following:
+\[ \partial_t f_s(t,x, v_x) - q_s\sqrt{\frac{m_e}{m_s}} E \partial_{v_x} f_s(t,x, v_x) = 0, \\ \] +
+on \(\Omega = [0, 2\pi]\times[-10, 10]\) with
++\[\left\{ \begin{aligned} & f_0(x, v_x) = \exp\left(-\frac{1}{2}v^2\right), \\ & A(x, v_x) = - q_s\sqrt{\frac{m_e}{m_s}} E. \end{aligned} \right. \] +
+We test it on a grid \(N_x\times N_{v_x} = 50\times100\) with \(dt = 0.1\). The simulation runs on \(t\in[0,0.1]\) and the relative error is expected to be below \( 1*10^{-5}\).
+./testcollisions.sh input_params_ion_1x1x1x128x64.yaml
Test the interpolator on mesh points where the errors are supposed to be exact (machine error) and test the interpolator on "pseudo-random" points where the errors are supposed to be order 4 with a cubic bsplines basis.
-test_convergence.py
: compute the convergence order in space for the tests where the errors are not supposed to be exact.The tests implemented in this folder test the 2D polar advection operator implemented in the src/geometryRTheta/advection/
folder ( Advection operator ).
The tests are made for different parameters which are:
-