We present a finite volume method for the solution of the two-dimensional Poisson equation ∇· (β(x)∇u(x)) = f(x) with variable, discontinuous coefficients and solution discontinuities on irregular domains. The method uses bilinear ansatz functions on Cartesian grids for the solution u(x) resulting in a compact nine-point stencil. The resulting linear problem has been solved with a standard mult...

We have developed a communication optimizer that concentrates on stencil communication patterns. This optimizer has been done in the context of the UNH C* compiler that targets distributed-memory MIMD computers. Our work has two distinguishing features: The compiler/optimizer is designed to be highly portable. We achieve this goal by providing eecient support for the optimizations in the run-ti...

This report documents the program and the outcomes of Dagstuhl Seminar 15161 “Advanced Stencil-Code Engineering”. The seminar was hosted by the DFG project with the same name (ExaStencils for short) in the DFG priority programme “Software for Exascale Computing” (SPPEXA). It brought together experts from mathematics, computer science and applications to explore the challenges of very high perfo...

In this paper, we propose an augmented coupling interface method on a Cartesian grid for solving eigenvalue problems with sign-changed coefficients. The underlying idea of the method is the correct local construction near the interface which incorporates the jump conditions. Themethod,which is very easy to implement, is based onfinite difference discretization. Themain ingredients of the propos...

SUMMARY The MultiScale Finite-Volume (MSFV) method is known to produce non-monotone solutions. The causes of the non-monotone solutions are identified and connected to the local flux across the boundaries of primal coarse cells induced by the basis functions. We propose a monotone MSFV (m-MSFV) method based on a local stencil-fix that guarantees monotonicity of the coarse-scale operator, and th...

This paper introduces a two-dimensional cell-centred finite volume discretization of the Poisson problem on adaptive Cartesian quadtree grids which exhibits second order accuracy in both the solution and its gradients, and requires no grading condition between adjacent cells. At T-junction configurations, which occur wherever resolution differs between neighbouring cells, use of the standard ce...

First order methods are commonly used in numerical simulations of gas-solids fluidized beds because they are both stable and affordable. Unfortunately, because of the large amounts of numerical diffusion inherent to these methods higher order methods are recommended to accurately predict bed dynamics e.g., voids or bubbles. The deferred correction method and the downwind factor method are both ...

In this research, an efficient Galerkin Finite Volume Method (GFVM) along with the h–refinement adaptive process and post–processing error estimation analysis is presented for fracture analysis. The adaptive strategy is used to produce more accurate solution with the least computational cost. To investigate the accuracy and efficiency of the developed model, the GFVM is compared with two versio...