CPDES2: A preconditioned conjugate gradient solver for linear asymmetric matrix equations arising from coupled partial differential equations in two dimensions

Abstract
Many physical problems require the solution of coupled partial differential equations 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 b...

Title of program: CPDES2
Catalogue Id: ABFD_v1_0

Nature of problem
Certain coupled elliptic and parabolic partial differential equations that arise in plasma physics and other applications are to be solved in two dimensions. The implicit solution techniques used for these equations give rise to a system of linear equations whose matrix operator is sparse (with a complicated subband structure) and generally asymmetric. We provide a fully vectorized algorithm for their solution.

Versions of this program held in the CPC repository in Mendeley Data
ABFD_v1_0; CPDES2; 10.1016/0010-4655(88)90152-X

This program has been imported from the CPC Program Library held at Queen's University Belfast (1969-2019)

摘要
众多物理问题需要求解二维域上的耦合偏微分方程。当关注的时标要求对方程进行隐式离散化时，需解决一个相当复杂的全局矩阵系统。矩阵的确切形式取决于空间网格的选择以及所采用的有限元或有限差分近似。CPDES2 允许每个空间算子拥有5或9点模板，并允许进行一般耦合...
程序名称：CPDES2
目录编号：ABFD_v1_0
问题性质
在等离子体物理学和其他应用中产生的某些耦合椭圆型和抛物型偏微分方程，需在二维空间内求解。用于这些方程的隐式求解技术导致了一个线性方程组，其矩阵算子是稀疏的（具有复杂的子带结构）且通常是非对称的。我们提供了一种针对其求解的完全向量化算法。
Mendeley数据中 CPC 仓库中保存的此程序的版本
ABFD_v1_0; CPDES2; 10.1016/0010-4655(88)90152-X
本程序已从贝尔法斯特女王大学（1969-2019）保存的 CPC 程序库中导入。