A Scalable Paradigm for Effectively-Dense Matrix Formulated Applications

There is a class of problems in computational science and engineering which require formulation in full matrix form and which are generally solved as dense matrices either because they are dense or because the sparsity can not be easily exploited. Problems such as those posed by computational electromagnetics, computational chemistry and some quantum physics applications frequently fall into this class. It is not sufficient just to solve the matrix problem for these applications as other components of the calculation are usually of equal computational load on current computer systems, and these components are consequently of equal importance to the end user of the application. We describe a general method for programming such applications using a combination of distributed computing systems and of more powerful back-end compute resources to schedule the components of such applications. We show how this not only improves computational performance but by making more memory available, allows hitherto impracticably large problems to be run. We illustrate this problem paradigm and our method of solution with problems in electromagnetics, chemistry and physics, and give a detailed performance analysis of a typical electromagnetics application. We discuss a method for scheduling the computational components using the Application Visualisation System (AVS).

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