Alternating-Direction Line-Relaxation Methods on Multicomputers

We study the multicom.puter performance of a three-dimensional Navier–Stokes solver based on alternating-direction line-relaxation methods. We compare several multicomputer implementations, each of which combines a particular line-relaxation method and a particular distributed block-tridiagonal solver. In our experiments, the problem size was determined by resolution requirements of the application. As a result, the granularity of the computations of our study is finer than is customary in the performance analysis of concurrent block-tridiagonal solvers. Our best results were obtained with a modified half-Gauss–Seidel line-relaxation method implemented by means of a new iterative block-tridiagonal solver that is developed here. Most computations were performed on the Intel Touchstone Delta, but we also used the Intel Paragon XP/S, the Parsytec SC-256, and the Fujitsu S-600 for comparison

Fast and accurate computation of the logarithmic capacity of compact sets

We present a numerical method for computing the logarithmic capacity of compact subsets of $\mathbb{C}$, which are bounded by Jordan curves and have finitely connected complement. The subsets may have several components and need not have any special symmetry. The method relies on the conformal map onto lemniscatic domains and, computationally, on the solution of a boundary integral equation with the Neumann kernel. Our numerical examples indicate that the method is fast and accurate. We apply it to give an estimate of the logarithmic capacity of the Cantor middle third set and generalizations of it

Efficient implicit FEM simulation of sheet metal forming

For the simulation of industrial sheet forming processes, the time discretisation is\ud one of the important factors that determine the accuracy and efficiency of the algorithm. For\ud relatively small models, the implicit time integration method is preferred, because of its inherent\ud equilibrium check. For large models, the computation time becomes prohibitively large and, in\ud practice, often explicit methods are used. In this contribution a strategy is presented that enables\ud the application of implicit finite element simulations for large scale sheet forming analysis.\ud Iterative linear equation solvers are commonly considered unsuitable for shell element models.\ud The condition number of the stiffness matrix is usually very poor and the extreme reduction\ud of CPU time that is obtained in 3D bulk simulations is not reached in sheet forming simulations.\ud Adding mass in an implicit time integration method has a beneficial effect on the condition number.\ud If mass scaling is used—like in explicit methods—iterative linear equation solvers can lead\ud to very efficient implicit time integration methods, without restriction to a critical time step and\ud with control of the equilibrium error in every increment. Time savings of a factor of 10 and more\ud can easily be reached, compared to the use of conventional direct solvers.\ud