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CPDES2: A preconditioned conjugate gradient solver for linear asymmetric matrix equations arising from coupled partial differential equations in two dimensions. (English) Zbl 0812.65091

Summary: Many physical problems require the solution of coupled partial differential equations (PDE’s) on two-dimensional domains. When the time scales of interest dictate an implicit discretization of the equations a rather complicated global matrix system needs solution. The exact form of the matrix depends on the choice of spatial grids and on the finite element or finite difference approximations employed. CPDES2 allows each spatial operator to have 5 or 9 point stencils and allows for general couplings between all of the component PDE’s and it automatically generates the matrix structures needed to perform the algorithm.
The resulting sparse matrix equation is solved by either the preconditioned conjugate gradient method or by the preconditioned biconjugate gradient algorithm. An arbitrary number of component equations are permitted only limited by available memory. In the sub-band representation used, we generate an algorithm that is written compactly in terms of indirect indices which is vectorizable on some of the newer scientific computers.

MSC:

65N22 Numerical solution of discretized equations for boundary value problems involving PDEs
65N06 Finite difference methods for boundary value problems involving PDEs
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65F10 Iterative numerical methods for linear systems
35J25 Boundary value problems for second-order elliptic equations
35K20 Initial-boundary value problems for second-order parabolic equations

Software:

ILUBCG2; CPDES2
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Full Text: DOI

References:

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