DISCRETIZATION |
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5 POINT STAR | Standard finite differences |
7 POINT STAR | Standard finite differences in 3D (boxes) |
COLLOCATION | Collocation by Hermite piecewise bicubic elements |
INTERIOR COLLOCATION | Collocation (rectangles) + uncoupled boundary conditions |
HERMITE COLLOCATION | Collocation (rectangles) |
SPLINE GALERKIN | Galerkin, General piecewise polynomials (rectangles) |
HODIE | High order finite method, (rectangles) |
HODIE HELMHOLTZ | Fast HODIE for Helmholtz problems |
INDEXING |
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RED BLACK | Red-black ordering of finite difference equations |
MINIMUM DEGREE | Minimum degree ordering of equations |
REVERSE CUTHILL MCKEE | Reduce bandwidth of linear systems |
NESTED DISSECTION | Very efficient ordering for Gauss elimination |
INTERIOR COLLORDER | Reorder INTERIOR COLLOCATION equations |
HERMITE COLLORDER | Reorder HERMITE COLLOCATION equations |
SOLUTION |
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LINPACK BAND | LINPACK band matrix solver |
LINPACK SPD BAND | LINPACK for symmetric positive definite band matrix |
BAND GE | LINPACK BAND with scaled partial pivoting |
BAND GE NO PIVOTING | LINPACK BAND with no pivoting at all |
ENVELOPE LDLT | Envelope elimination for symmetric band matrices |
ENVELOPE LDU | Envelope elimination for band matrices |
SOR | Successive overrelaxation |
JACOBI SI | Jacobi iteration with Semi-Iterative (SI) acceleration |
JACOBI CG | Jacobi iteration with Conjugate Gradient (CG) acceleration |
SYMMETRIC SOR SI | Line SOR with SI acceleration |
SYMMETRIC SOR CG | Line SOR with CG acceleration |
REDUCED SYSTEM | Iteration for red black ordering, SI acceleration |
REDUCED SYSTEM CG | Iteration for red black ordering, CG acceleration |
SPARSE LU PIVOTING | Sparse factorization with pivoting |
SPARSE GE NO PIVOTING | Sparse Gauss elimination with no pivoting |
SPARSE LU UNCOMPRESSED | Sparse matrix factorization, no pivoting |
SPARSE LU COMPRESSED | SPARSE LU, compressed storage scheme |
SPARSE LDLT | Sparse matrix factorization, symmetric matrices |
TRIPLE |
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HODIE 27 POINT 3D | High order differences, tensor product solution |
FFT 9 POINT | Fast Fourier Transforms methods |
P2C0 TRIANGLES | Galerkin method, biquadratic polynomials on triangles |
MARCHING ALGORITHM | Generalized marching algorithm |
DYAKANOV CG | Finite Differences, DYAKANOV conjugate gradient solution |
DYAKANOV CG 4 | Fourth order extrapolation of DYAKANOV CG |
FISHPAK HELMHOLTZ | FISHPAK cyclic reduction method for Helmholtz equation |
SET U BY BLENDING | Initialize u(x,y) |
SET U BY BICUBICS | Initialize u(x,y) |
MULTIGRID MG00 | Multigrid method for aUXX + bUYY + f U = g |
HODIE FFT | High order differences + FFT |
HODIE FFT 3D | HODIE FFT in 3 dimensions |
PROCEDURE |
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EIGENVALUES | Compute eigenvalues of discretization matrix |
SET UNKNOWN FOR 5 POINT STAR | Initialize u(x,y) for iteration methods |
DISPLAY MATRIX PATTERN | Print pattern of non-zeros in discretization matrix |
REMOVE BLENDED BC | Change PDE by subtracting from u(x,y) |
REMOVE BICUBIC BC | Change PDE by subtracting from u(x,y) |