Overlapping schwarz methods on unstructured meshes using non-matching coarse grids.

The majority of finite element models in structural engineering are composed of unstructured meshes. These unstructured meshes are often very large and require significant computational resources; hence they are excellent candidates for massively parallel computation. Parallel solution of the sparse matrices that arise from such meshes has been studied heavily, and many good algorithms have bee...

The issue of mesh quality for unstructured triangular and tetrahedral meshes is considered. The theoretical background to finite element methods is used to understand the basis of present-day geometrical mesh quality indicators. Simple tetrahedral mesh quality measures using both geometrical and solution information are described. Some of the issues in mesh quality for unstructured tetrahedral ...

The monodomain equations model the propagation of the action potential in the human heart : a very sharp pulse propagating at a high speed, which computation require fine unstructured 3D meshes. It is a non linear parabolic PDE of reaction diffusion type, coupled to one or several ODE, with multiple time-scales. Numerical difficulties, such as unstructured meshes and stability are addressed her...

A simple methodology that enables exact sensitivity analysis with unstructured meshes is presented. Using automatic differentiation, derivatives of highly non-linear state equations and cost functionals can be computed up to numerical precision. But with unstructured meshes, the nodal sensitivities, which are needed to perform the differentiation with respect to shape of the computational domai...

In the present paper, we introduce theH-wavelet method for the fast solution of nonlocal operator equations on unstructured meshes. On the given mesh, we construct a wavelet basis which provides vanishing moments with respect to the traces of polynomials in the space. With this basis at hand, the system matrix in wavelet coordinates is compressed to O(N logN) relevant matrix coefficients, where...

The use of unstructured adaptive tetrahedral meshes in the solution of transient flows poses a challenge for parallel computing due to the irregular and frequently changing nature of the data and its distribution. A parallel mesh adaptation algorithm, PTETRAD, for unstructured tetrahedral meshes (based on the serial code TETRAD) is described and analysed. The portable implementation of the para...

This paper presents a parallel finite element toolbox for computing large electromagnetic devices on unstructured tetrahedral meshes, FEMAG—Fem for ElectroMagnetics on Adaptive Grids. The finite element toolbox deals with unstructured tetrahedral meshes and can solve electromagnetic eddy current problems in both frequency domain and time domain. It adopts high-order edge element methods and ref...