Anderson, D. V.; Koniges, A. E.; Shumaker, D. E. CPDES2: A preconditioned conjugate gradient solver for linear asymmetric matrix equations arising from coupled partial differential equations in two dimensions. (English) Zbl 0812.65091 Comput. Phys. Commun. 51, No. 3, 391-403 (1988). 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 Keywords:implicit discretization; finite element; finite difference; sparse matrix equation; preconditioned biconjugate gradient algorithm Software:ILUBCG2; CPDES2 PDFBibTeX XMLCite \textit{D. V. Anderson} et al., Comput. Phys. Commun. 51, No. 3, 391--403 (1988; Zbl 0812.65091) Full Text: DOI References: [1] Horowitz, E. J.; Anderson, D. V.; Shumaker, D. E., Bull. Am. Phys. Soc., 30, 1565 (1985) [2] Europhysics Conference Abstracts, 10C, 353 (1986), Part I [3] Anderson, D. V.; Koniges, A. E.; Shumaker, D. E., Comput. Phys. Commun., 51, 405 (1988) [4] Shestakov, A. I.; Anderson, D. V., Comput. Phys. Commun., 30, 31 (1983) [5] Anderson, D. V., Comput. Phys. Commun., 30, 43 (1983) [6] Koniges, A. E.; Anderson, D. V., Comput. Phys. Commun., 43, 297 (1986) [7] Meijerink, J. A.; van der Vorst, H. A., Math. Comp., 31, 148 (1977) [8] Kershaw, D. S., J. Comput. Phys., 26, 43 (1978) [9] Kershaw, D. S., J. Comput. Phys., 38, 114 (1980) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.