OpenMG: A new multigrid implementation in Python. (English) Zbl 1349.65116

Bertalan, Tom S.; Islam, Akand W.; Sidje, Roger B.; Carlson, Eric S.

Numer. Linear Algebra Appl. 21, No. 5, 685-700 (2014).

Summary: In many large-scale computations, systems of equations arise in the form \(Au=b\), where \(A\) is a linear operation to be performed on the unknown data \(u\), producing the known right-hand side, \(b\), which represents some constraint of known or assumed behavior of the system being modeled. Because such systems can be very large, solving them directly can be too slow. In contrast, a multigrid method removes different components of the error at different resolutions using smoothers that reduce high-frequency components of the error more readily than low. Here, we present an open-source multigrid solver written only in Python. OpenMG is a pure Python experimentation environment for testing multigrid concepts, not a production solver. The particular restriction method implemented is for ‘standard’ multigrid. By making the code simple and modular, we make the algorithmic details clear. The resulting solver is tested on an implicit pressure reservoir simulation problem with satisfactory results.

MSC:

65F10	Iterative numerical methods for linear systems
76S05	Flows in porous media; filtration; seepage
65N55	Multigrid methods; domain decomposition for boundary value problems involving PDEs
65Y15	Packaged methods for numerical algorithms

Keywords:

Python; multigrid; NumPy; partial differential equation; implicit pressure reservoir simulation

Software:

NumPy; OpenMG; PyAMG; Python; SciPy