Diffusion2D

<electrical solver="Diffusion2D">

Corresponding Python class: electrical.diffusion.Diffusion2D.

Two-dimensional diffusion solver in Cartesian geometry.

Attributes:

• name (required) – Solver name.

Contents:

<geometry>

Geometry for use by this solver.

Attributes:

• ref (required) – Name of a Cartesian2D geometry defined in the <geometry> section.

<mesh>

Optional Rectangular2D, Ordered, Regular mesh used by this solver.

Attributes:

• ref (required) – Name of a Rectangular2D, Ordered, Regular mesh defined in the <grids> section.

<loop>

Configuration of the self-consistent loop.

Attributes:

• maxerr – Maximum allowed current density error. (float (%), default 0.05 %)

<matrix>

Matrix solver configuration.

Attributes:

• algorithm – Algorithm used for solving set of linear positive-definite equations. (cholesky, gauss, or iterative, default is cholesky)

<iterative>

Parameters for iterative matrix solver. PLaSK uses NSPCG package for performing iterations. Please refer to its documentation for explanation of most of the settings.

Attributes:

• maxit – Maximum number of iterations. (int, default 1000)

• maxerr – Maximum iteration error. (float, default 1e-6)

• noconv – Desired behavior if the iterative solver does not converge. (error, warning, or continue, default is warning)

• accelerator – Accelerator used for iterative matrix solver. (cg, si, sor, srcg, srsi, basic, me, cgnr, lsqr, odir, omin, ores, iom, gmres, usymlq, usymqr, landir, lanmin, lanres, cgcr, or bcgs, default is cg)

• preconditioner – Preconditioner used for iterative matrix solver. (rich, jac, ljac, ljacx, sor, ssor, ic, mic, lsp, neu, lsor, lssor, llsp, lneu, bic, bicx, mbic, or mbicx, default is ic)

• nfact – This number initializes the frequency of partial factorizations. It specifies the number of linear system evaluations between factorizations. The default value is 1, which means that a factorization is performed at every iteration. (int, default 10)

• ndeg – Degree of the polynomial to be used for the polynomial preconditioners. (int, default 1)

• lvfill – Level of fill-in for incomplete Cholesky preconditioners. Increasing this value will result in more accurate factorizations at the expense of increased memory usage and factorization time. (int, default 0)

• ltrunc – Truncation bandwidth to be used when approximating the inverses of matrices with dense banded matrices. An increase in this value means a more accurate factorization at the expense of increased storage. (int, default 0)

• omega – Relaxation parameter. (float, default 1.0)

• nsave – The number of old vectors to be saved for the truncated acceleration methods. (int, default 5)

• nrestart – The number of iterations between restarts for the restarted acceleration methods. (int, default 100000)

Preconditioner choices:

rich	Richardson’s method
jac	Jacobi method
ljac	Line Jacobi method
ljacx	Line Jacobi method (approx. inverse)
sor	Successive Overrelaxation
ssor	Symmetric SOR (can be used only with SOR accelerator)
ic	Incomplete Cholesky (default)
mic	Modified Incomplete Cholesky
lsp	Least Squares Polynomial
neu	Neumann Polynomial
lsor	Line SOR
lssor	Line SSOR
llsp	Line Least Squares Polynomial
lneu	Line Neumann Polynomial
bic	Block Incomplete Cholesky (ver. 1)
bicx	Block Incomplete Cholesky (ver. 2)
mbic	Modified Block Incomplete Cholesky (ver. 1)
mbicx	Modified Block Incomplete Cholesky (ver. 2)

Accelerator choices:

cg	Conjugate Gradient acceleration (default)
si	Chebyshev acceleration or Semi-Iteration
sor	Successive Overrelaxation (can use only SOR preconditioner)
srcg	Symmetric Successive Overrelaxation Conjugate Gradient Algorithm (can use only SSOR preconditioner)
srsi	Symmetric Successive Overrelaxation Semi-Iteration Algorithm (can use only SSOR preconditioner)
basic	Basic Iterative Method
me	Minimal Error Algorithm
cgnr	Conjugate Gradient applied to the Normal Equations
lsqr	Least Squares Algorithm
odir	ORTHODIR, a truncated/restarted method useful for nonsymmetric systems of equations
omin	ORTHOMIN, a common truncated/restarted method used for nonsymmetric systems
ores	ORTHORES, another truncated/restarted method for nonsymmetric systems
iom	Incomplete Orthogonalization Method
gmres	Generalized Minimal Residual Method
usymlq	Unsymmetric LQ
usymqr	Unsymmetric QR
landir	Lanczos/ORTHODIR
lanmin	Lanczos/ORTHOMIN or Biconjugate Gradient Method
lanres	Lanczos/ORTHORES or “two-sided” Lanczos Method
cgcr	Constrained Generalized Conjugate Residual Method
bcgs	Biconjugate Gradient Squared Method