# File invert_laplace.cxx¶

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 $$x$$ and $$x$$ are perpendicular (X-Z) or 3D fields, and $$a$$ and d are 2D fields. If d is not supplied then it is 1

Flags control the boundary conditions (see header file)

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/.

Functions

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

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

int invert_laplace(const FieldPerp &b, FieldPerp &x, int flags, const Field2D *a, const Field2D *c, const Field2D *d)
int invert_laplace(const Field3D &b, Field3D &x, int flags, const Field2D *a, const Field2D *c, const Field2D *d)
const Field3D invert_laplace(const Field3D &b, int flags, const Field2D *a, const Field2D *c, const Field2D *d)

More readable API for calling Laplacian inversion. Returns x.