Simulating the propagation of 3D ultrasonic waves in a nonlinear medium is a demanding task. It requires the solution of time-dependent and nonlinear partial differential equations (PDEs). For such nonlinear PDEs, we have to use an implicit numerical method that is very CPU-intensive. Parallel simulation is therefore essential for studying those ultrasonic waves with satisfactory accuracy. We present in this paper the parallelization of an ultrasonic wave simulator and report some numerical experiments that have been run on a 24-node Linux cluster. Our CPU-measurements indicate that Linux clusters can deliver satisfactory parallel computing power for the numerical solution of PDEs. For simulating 3D ultrasonic waves in particular, we have found that our Linux cluster, which consists of 48 Pentium-III 500MHz processors inter-connected with a 100Mbit/s ethernet network, is fully comparable with an SGI Origin 2000 machine.

Introduction For low-cost PC clusters that are made up of only o-the-shelf components, a common notion is that they can not be real competitors for conventional supercomputers in respect of delivering sustained computing power. We aim to show in the present paper that this needs not be the case, especially when PC clusters are used to solve partial dierential equations (PDEs). More specically, we will look at the issue of how to achieve good PDE solving performance on PC clusters, and present several case studies for a particular Linux cluster of 48 Pentium-III processors. The study of many physical phenomena resorts to the numerical solution of certain PDEs. To achieve a satisfactory resolution, it is often necessary to use millions of degrees of freedom. Such large scale computations demand huge computing power, which is traditionally provided by supercomputers. However, recent research in the eld of cluster computing has indicated that PC clusters can be an attractive

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