Matrix-free methods in two-phase flow simulations on graphics processors

Karl Ljungkvist
Division of Scientific Computing
Department of Information Technology
Uppsala University


When simulating two-phase flows, the underlying partial differential equations are typically discretized using high-order finite-element methods. For relevant problems in 3D involving millions or even billions of degrees of freedom, the resulting system matrix is too large store in memory, making it necessary to employ matrix-free methods to solve the discrete system. In the matrix-free formulation, the matrix-vector products at the core of any iterative solver, fall apart into many smaller constituents, which can be processed in parallel. In this talk, I will describe ongoing work on a matrix-free iterative solver, leveraging graphics processors for the matrix-free products.