Solving Partial Differential Equations on Parallel Computers

Numerical simulation of fluid dynamic problems on distributed memory parallel computers

“…However, these peak execution rates are very difficut to achieve or sustain in realistic codes. It is not unusual, in practice, to have a sustained rate which is only 10-20% of the peak performance [2]. Next, the Delta uses a distributed MIMD architecture: communication is required when more than one node is used to perform a given task.…”

“…Using the data f, Q and g defined by (2) and (3) As mentioned earlier, since the discretization is static and regular, the nodes can be load balanced at the start of the code by ensuring that each subdomain contains the same number of grid points. The algorithm simply consists of steps that concurrently update the processor subregions, separated by communication steps that involve the swapping of edge values between neighboring processors.…”

Solving high Reynolds-number viscous flows by the general BEM and domain decomposition method

“…in the subdomain I , we have a system of algebraic equations of the form B I x I = c I ; I = 1; 2; : : : ; M (27) where the superscript I denotes the subdomain I , M is the number of subdomains, and…”

“…Each of the M local matrix systems given by Equation (27) can be assembled with its neighbouring systems according to the matching conditions given by Equations (31)-(34).…”

“…If each subdomain is assigned a processor, it is very convenient to parallelize our approach. This parallelization strategy is often employed in domain decomposition parallel computation [27]. In this paper, to make the GBEM numerically more e cient, we combine the DDM with the data decomposition parallelization strategy [28] in each subdomain.…”