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

**Karl Ljungkvist
**

Division of Scientific Computing

Department of Information Technology

Uppsala University

### Abstract:

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.