Nonlinear inviscid water wave computations are performed using an Euler-Lagrange approach to solve a boundary integral formaulation. the integral equations are solved numerically at each time step using a desingularized method with multipole acceleration. Solutions obtained using multipole acceleration can require as little as O(N) effort and O(N) storage whereas conventional methods require O(N~2) effort and storage. Multipole methods are applicable to a variety of physical simulation problems in astrophysics, plasma physics, molecular dynamics, electrostatics, and fluid dynamics. The application of multipole methods to the numerical solutions of these problems has the potential of significantly improving computational efficiency.
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