Hilmar Wobker

Using GPUs to improve multigrid solver performance on a cluster

This paper explores the coupling of coarse and fine-grained parallelism for Finite Element (FE) simulations based on efficient parallel multigrid solvers. The focus lies on both system performance and a minimally invasive integration of hardware acceleration into an existing software package, requiring no changes to application code. Because of their excellent price performance ratio, we demonstrate the viability of our approach by using commodity Graphics Processing Units (GPUs), addressing the issue of limited precision on GPUs by applying a mixed precision, iterative refinement technique. Our results show that we do not compromise any software functionality and gain speedups of two and more for large problems.

GPU acceleration of an unmodified parallel finite element Navier-Stokes solver

We have previously suggested a minimally invasive approach to include hardware accelerators into an existing large-scale parallel finite element PDE solver toolkit, and implemented it into our software FEAST. Our concept has the important advantage that applications built on top of FEAST benefit from the acceleration immediately, without changes to application code. In this paper we explore the limitations of our approach by accelerating a Navier-Stokes solver. This nonlinear saddle point problem is much more involved than our previous tests, and does not exhibit an equally favourable acceleration potential: Not all computational work is concentrated inside the linear solver. Nonetheless, we are able to achieve speedups of more than a factor of two on a small GPU-enhanced cluster. We conclude with a discussion how our concept can be altered to further improve acceleration.

Numerical Benchmarking of Fluid-Structure Interaction: A Comparison of Different Discretization and Solution Approaches

Comparative benchmark results for different solution methods for fluid-structure interaction problems are given which have been developed as collaborative project in the DFG Research Unit 493. The configuration consists of a laminar incompressible channel flow around an elastic object. Based on this benchmark configuration the numerical behavior of different approaches is analyzed exemplarily. The methods considered range from decoupled approaches which combine Lattice Boltzmann methods with hp-FEM techniques, up to strongly coupled and even fully monolithic approaches which treat the fluid and structure simultaneously.

Co-processor acceleration of an unmodified parallel solid mechanics code with FEASTGPU

We have previously presented an approach to include graphics processing units as co-processors in a parallel Finite Element multigrid solver called FEAST. In this paper we show that the acceleration transfers to real applications built on top of FEAST, without any modifications of the application code. The chosen solid mechanics code is well suited to assess the practicability of our approach due to higher accuracy requirements and a more diverse CPU/co-processor interaction. We demonstrate in detail that the single precision execution of the co-processor does not affect the final accuracy, and analyse how the local acceleration gains of factors 5.5-9.0 translate into 1.6- to 2.6-fold total speed-up.

Numerical Simulation and Benchmarking of a Monolithic Multigrid Solver for Fluid-Structure Interaction Problems with Application to Hemodynamics

An Arbitrary Lagrangian-Eulerian (ALE) formulation is applied in a fully coupled monolithic way, considering the fluid-structure interaction (FSI) problem as one continuum. The mathematical description and the numerical schemes are designed in such a way that general constitutive relations (which are realistic for biomechanics applications) for the fluid as well as for the structural part can be easily incorporated. We utilize the LBB-stable finite element pairs Q 2 P 1 and P 2 + P 1 for discretization in space to gain high accuracy and perform as time-stepping the 2nd order Crank-Nicholson, respectively, a new modified Fractional-Step-θ-scheme for both solid and fluid parts. The resulting discretized nonlinear algebraic system is solved by a Newton method which approximates the Jacobian matrices by a divided differences approach, and the resulting linear systems are solved by direct or iterative solvers, preferably of Krylov-multigrid type.