Matthias MaishackBrunel University
Title: p-FEM and p-BEM -- achieving high accuracy
Abstract: It is well known, that we can achieve exponential fast convergence by approximating the solution of a pde using either the p-version fem or bem if then solution is smooth, or using the hp-version with geometrical refined mesh if the solution has singularities. Achieving exponential fast convergence asymptotically proves to be surprisingly difficult, due to requirements on memory, solution time and the necessary numerical precision. In this presentation we investigate changes necessary to an existing fem/bem code, software tools for converting the code to a different data type using a multi-precision package and discuss implementation issues which arise from considerable more time and memory consuming arithmetic operations. We will compare standard double precision (hardware supported), quad precision (compiler supported) and higher precision (additional Software package ). We will present examples achieving errors with 1e-30 or less using p- and hp fem-bem methods in 1,2 and 3 dimensions.
Konstatinos ZygalakisUniversity of Southampton & EPFL
Qualitative Behaviour of Numerical Methods for SDEs and Applications
Patrick LamUniversity of Waterloo, Canada
‘Views, Programming Languages Research, and HPC’