File invert_laplace.hxx#

Perpendicular Laplacian inversion using FFT and Tridiagonal solver

Equation solved is: \(d*\nabla^2_\perp x + (1/c)\nabla_perp c\cdot\nabla_\perp x + a x = b\)

Where a, c and d are functions of x and y only (not z)

Copyright 2010 B.D.Dudson, S.Farley, M.V.Umansky, X.Q.Xu

Contact: Ben Dudson, bd512@york.ac.uk

This file is part of BOUT++.

BOUT++ is free software: you can redistribute it and/or modify it under the terms of the GNU Lesser General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version.

BOUT++ is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more details.

You should have received a copy of the GNU Lesser General Public License along with BOUT++. If not, see http://www.gnu.org/licenses/.

Defines

PVEC_REAL_MPI_TYPE

Typedefs

using RegisterLaplace = LaplaceFactory::RegisterInFactory<DerivedType>#

Simpler name for Factory registration helper class

Usage: 

#include <bout/laplacefactory.hxx>
namespace {
RegisterLaplace<MyLaplace> registerlaplacemine("mylaplace");
}

using RegisterUnavailableLaplace = LaplaceFactory::RegisterUnavailableInFactory#

Functions

void laplace_tridag_coefs(int jx, int jy, int jz, dcomplex &a, dcomplex &b, dcomplex &c, const Field2D *ccoef = nullptr, const Field2D *d = nullptr, CELL_LOC loc = CELL_DEFAULT)

Returns the coefficients for a tridiagonal matrix for laplace. Used by Delp2 too.

Variables

constexpr auto LAPLACE_SPT = "spt"#
constexpr auto LAPLACE_TRI = "tri"#
constexpr auto LAPLACE_BAND = "band"#
constexpr auto LAPLACE_PETSC = "petsc"#
constexpr auto LAPLACE_PETSCAMG = "petscamg"#
constexpr auto LAPLACE_PETSC3DAMG = "petsc3damg"#
constexpr auto LAPLACE_HYPRE3D = "hypre3d"#
constexpr auto LAPLACE_CYCLIC = "cyclic"#
constexpr auto LAPLACE_MULTIGRID = "multigrid"#
constexpr auto LAPLACE_NAULIN = "naulin"#
constexpr auto LAPLACE_IPT = "ipt"#
constexpr auto LAPLACE_PCR = "pcr"#
constexpr auto LAPLACE_PCR_THOMAS = "pcr_thomas"#
constexpr int INVERT_DC_GRAD = 1#

Zero-gradient for DC (constant in Z) component. Default is zero value.

constexpr int INVERT_AC_GRAD = 2#

Zero-gradient for AC (non-constant in Z) component. Default is zero value.

constexpr int INVERT_AC_LAP = 4#

Use zero-laplacian (decaying solution) to AC component.

constexpr int INVERT_SYM = 8#

Use symmetry to enforce either zero-value or zero-gradient.

constexpr int INVERT_SET = 16#

Set boundary to value.

constexpr int INVERT_RHS = 32#

Use input value in RHS boundary.

constexpr int INVERT_DC_LAP = 64#

Use zero-laplacian solution for DC component.

constexpr int INVERT_BNDRY_ONE = 128#

Only use one boundary point.

constexpr int INVERT_DC_GRADPAR = 256#
constexpr int INVERT_DC_GRADPARINV = 512#
constexpr int INVERT_IN_CYLINDER = 1024#

For use in cylindrical coordiate system.

constexpr int INVERT_ZERO_DC = 1#

Zero the DC (constant in Z) component of the solution.

constexpr int INVERT_START_NEW = 2#

Iterative method start from solution=0. Has no effect for direct solvers.

constexpr int INVERT_BOTH_BNDRY_ONE = 4#

Sets the width of the boundaries to 1.

constexpr int INVERT_4TH_ORDER = 8#

Use band solver for 4th order in x.

constexpr int INVERT_KX_ZERO = 16#

Zero the kx=0, n = 0 component.

class LaplaceFactory : public Factory<Laplacian, LaplaceFactory, Options*, CELL_LOC, Mesh*, Solver*>#

Public Functions

inline ReturnType create(Options *options = nullptr, CELL_LOC loc = CELL_CENTRE, Mesh *mesh = nullptr, Solver *solver = nullptr)#
inline ReturnType create(const std::string &type, Options *options) const#

Public Static Attributes

static constexpr auto type_name = "Laplacian"#
static constexpr auto section_name = "laplace"#
static constexpr auto option_name = "type"#
static constexpr auto default_type = LAPLACE_CYCLIC#
class Laplacian#
#include <invert_laplace.hxx>

Base class for Laplacian inversion.

Subclassed by LaplaceHypre3d, LaplaceNaulin, LaplacePCR, LaplacePCR_THOMAS, LaplacePetsc, LaplacePetsc3dAmg, LaplaceSerialTri, LaplaceSPT

Public Functions

Laplacian(Options *options = nullptr, const CELL_LOC loc = CELL_CENTRE, Mesh *mesh_in = nullptr, Solver *solver = nullptr)#

Laplacian inversion initialisation. Called once at the start to get settings.

virtual ~Laplacian() = default#
virtual void setCoefA(const Field2D &val) = 0#

Set coefficients for inversion. Re-builds matrices if necessary.

inline virtual void setCoefA(const Field3D &val)#
inline virtual void setCoefA(BoutReal r)#
virtual void setCoefC(const Field2D &val) = 0#
inline virtual void setCoefC(const Field3D &val)#
inline virtual void setCoefC(BoutReal r)#
inline virtual void setCoefC1(const Field2D &val)#
inline virtual void setCoefC1(const Field3D &val)#
inline virtual void setCoefC1(BoutReal r)#
inline virtual void setCoefC2(const Field2D &val)#
inline virtual void setCoefC2(const Field3D &val)#
inline virtual void setCoefC2(BoutReal r)#
virtual void setCoefD(const Field2D &val) = 0#
inline virtual void setCoefD(const Field3D &val)#
inline virtual void setCoefD(BoutReal r)#
virtual void setCoefEx(const Field2D &val) = 0#
inline virtual void setCoefEx(const Field3D &val)#
inline virtual void setCoefEx(BoutReal r)#
virtual void setCoefEz(const Field2D &val) = 0#
inline virtual void setCoefEz(const Field3D &val)#
inline virtual void setCoefEz(BoutReal r)#
inline virtual void setGlobalFlags(int f)#
inline virtual void setInnerBoundaryFlags(int f)#
inline virtual void setOuterBoundaryFlags(int f)#
inline virtual bool uses3DCoefs() const#

Does this solver use Field3D coefficients (true) or only their DC component (false)

virtual FieldPerp solve(const FieldPerp &b) = 0#
virtual Field3D solve(const Field3D &b)#
virtual Field2D solve(const Field2D &b)#
inline virtual FieldPerp solve(const FieldPerp &b, const FieldPerp &x0)#
virtual Field3D solve(const Field3D &b, const Field3D &x0)#

Performs the laplacian inversion y-slice by y-slice

Parameters:

  • b – [in] All the y-slices of b_slice, which is the right hand side of the equation A*x_slice = b_slice

  • x0 – [in] All the y-slices of the variable eventually used to set BC

Returns:

x All the y-slices of x_slice in the equation A*x_slice = b_slice

virtual Field2D solve(const Field2D &b, const Field2D &x0)#
void tridagCoefs(int jx, int jy, int jz, dcomplex &a, dcomplex &b, dcomplex &c, const Field2D *ccoef = nullptr, const Field2D *d = nullptr, CELL_LOC loc = CELL_DEFAULT)#

Coefficients in tridiagonal inversion.

inline void outputVars(Options &output_options) const#

Add any output variables to output_options, for example, performance information, with optional name for the time dimension

inline virtual void outputVars(MAYBE_UNUSED(Options &output_options), MAYBE_UNUSED(const std::string &time_dimension)) const#
inline void savePerformance(Solver &solver)#

Register performance monitor with solver, prefix output with Options section name

void savePerformance(Solver &solver, const std::string &name)#

Register performance monitor that is call every timestep with solver, prefix output with name. Call this function from your PhysicsModel::init to get time-dependent performance information, or call outputVars directly in non-model code to get the information at that point in time.

To use this for a Laplacian implementation, override outputVars(Options&, const std::string&), and add whatever information you would like to save to the Options argument. This will then be called automatically by LaplacianMonitor.

See LaplaceNaulin::outputVars for an example.

inline std::string getPerformanceName() const#

Get name for writing performance information.

Public Static Functions

static inline std::unique_ptr<Laplacian> create(Options *opts = nullptr, const CELL_LOC location = CELL_CENTRE, Mesh *mesh_in = nullptr, Solver *solver = nullptr)#

Create a new Laplacian solver

Parameters:

opt – [in] The options section to use. By default “laplace” will be used

static Laplacian *defaultInstance()#

Return pointer to global singleton.

static void cleanup()#

Frees all memory.

Protected Functions

inline void tridagCoefs(int jx, int jy, BoutReal kwave, dcomplex &a, dcomplex &b, dcomplex &c, const Field2D *ccoef = nullptr, const Field2D *d = nullptr, CELL_LOC loc = CELL_DEFAULT)#
void tridagCoefs(int jx, int jy, BoutReal kwave, dcomplex &a, dcomplex &b, dcomplex &c, const Field2D *c1coef, const Field2D *c2coef, const Field2D *d, CELL_LOC loc = CELL_DEFAULT)#
inline void tridagMatrix(dcomplex *avec, dcomplex *bvec, dcomplex *cvec, dcomplex *bk, int jy, int kz, BoutReal kwave, int flags, int inner_boundary_flags, int outer_boundary_flags, const Field2D *a, const Field2D *ccoef, const Field2D *d, bool includeguards = true, bool zperiodic = true)#
void tridagMatrix(dcomplex *avec, dcomplex *bvec, dcomplex *cvec, dcomplex *bk, int jy, int kz, BoutReal kwave, int flags, int inner_boundary_flags, int outer_boundary_flags, const Field2D *a, const Field2D *c1coef, const Field2D *c2coef, const Field2D *d, bool includeguards = true, bool zperiodic = true)#

Set the matrix components of A in Ax=b

This function will

  1. Calling tridagCoef, solving

    D*Laplace_perp(x) + (1/C1)Grad_perp(C2)*Grad_perp(x) + Ax = B

    for each fourier component

  2. Set the boundary conditions by setting the first and last rows properly

Parameters:

  • avec – [in] Lower diagonal of the tridiagonal matrix. DO NOT CONFUSE WITH “A”

  • bvec – [in] The main diagonal

  • cvec – [in] The upper diagonal. DO NOT CONFUSE WITH “C” (called ccoef here)

  • bk – [in] The b in Ax = b

  • jy – [in] Index of the current y-slice

  • kz – [in] The mode number index

  • kwave – [in] The mode number (different from kz only if we are taking a part of the z-domain [and not from 0 to 2*pi])

  • global_flags – [in] Global flags of the inversion

  • inner_boundary_flags – [in] Flags used to set the inner boundary

  • outer_boundary_flags – [in] Flags used to set the outer boundary

  • a – [in] A in the equation above. DO NOT CONFUSE WITH avec

  • c1coef – [in] C1 in the equation above. DO NOT CONFUSE WITH cvec

  • c2coef – [in] C2 in the equation above. DO NOT CONFUSE WITH cvec

  • d – [in] D in the equation above

  • includeguards – [in] Whether or not the guard points in x should be used

  • zperiodic – [in] Whether a special case for kx=kz=0 is needed

  • avec – [out] Lower diagonal of the tridiagonal matrix. DO NOT CONFUSE WITH “A”

  • bvec – [out] The main diagonal

  • cvec – [out] The upper diagonal. DO NOT CONFUSE WITH “C” (called ccoef here)

inline void setPerformanceName(std::string name)#

Set the name for writing performance information.

Protected Attributes

bool async_send#

If true, use asyncronous send in parallel algorithms.

int maxmode#

The maximum Z mode to solve for.

bool low_mem#

If true, reduce the amount of memory used.

bool all_terms#

applies to Delp2 operator and laplacian inversion

bool nonuniform#

Non-uniform mesh correction.

bool include_yguards#

solve in y-guard cells, default true.

int extra_yguards_lower#

exclude some number of points at the lower boundary, useful for staggered grids or when boundary conditions make inversion redundant

int extra_yguards_upper#

exclude some number of points at the upper boundary, useful for staggered grids or when boundary conditions make inversion redundant

int global_flags#

Default flags.

int inner_boundary_flags#

Flags to set inner boundary condition.

int outer_boundary_flags#

Flags to set outer boundary condition.

CELL_LOC location#

staggered grid location of this solver

Mesh *localmesh#

Mesh object for this solver.

Coordinates *coords#

Coordinates object, so we only have to call localmesh->getCoordinates(location) once

Private Members

std::string performance_name#

Name for writing performance infomation; default taken from constructing Options section

LaplacianMonitor monitor = {*this}#

Private Static Attributes

static std::unique_ptr<Laplacian> instance = nullptr#

Singleton instance.

class LaplacianMonitor : public Monitor#

Public Functions

inline LaplacianMonitor(Laplacian &owner)#
int call(Solver *solver, BoutReal time, int iter, int nout) override#
void outputVars(Options &options, const std::string &time_dimension) override#

Private Members

Laplacian *laplacian = {nullptr}#