In this paper, we consider matrix-free finite-element techniques for efficient numerical solution of partial differential equations on modern manycore processors such as graphics cards. We present a GPU parallelization of a completely matrix-free geometric multigrid iterative solver, with support for general curved and adaptively refined meshes with hanging nodes. Comparing our implementation r...

A computational procedure based on a divergence-free H(div) method is presented for the Stokes and Navier-Stokes equations in this article. This method is designed to find velocity approximation in an exact divergence-free subspace of the corresponding H(div) finite element space. That is, the continuity equation is strongly enforced a priori and the pressure is eliminated from the calculation....

In this paper, mesh-free element free Galerkin (EFG) method is extended to solve two-dimensional potential flow problems. Two ideal fluid flow problems (i.e. flow over a rigid cylinder and flow over a sphere) have been formulated using variational approach. Penalty and Lagrange multiplier techniques have been utilized for the enforcement of essential boundary conditions. Four point Gauss quadra...