ELLPACK Problem Solving Modules


DISCRETIZATION

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

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

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

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

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)


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