Fast Boundary Integral Methods and Their Applications to Biological Problems

Integral Equations Methods: Fast Algorithms and Applications

Integral equations have long been an invaluable tool in the analysis of linear boundary value problems associated with the Laplace and Helmholtz equations, the equations of elasticity, the time-harmonic Maxwell equations, the Stokes equation, and many more. Numerical methods based on integral equations have become increasingly popular, due in large part to the development of associated fast alg...

Integral Equation Methods for Free Boundary Problems∗

We outline a unified approach for treating free boundary problems arising in Finance using integral equation methods. Starting with the PDE formulations of the free boundary problems, we show how to derive nonlinear integral equations for the free boundaries in a variety of Finance applications. Methods to treat theoretical (existence, uniqueness) questions and analytical and numerical approxim...

Sequential Methods and Their Applications

Multiscale Methods for Boundary Integral Equations and Their Application to Boundary Value Problems in Scattering Theory and Geodesy

SUMMARY In the present paper we give an overview on multiscale algorithms for the solution of boundary integral equations which are based on the use of wavelets. These methods have been introduced rst by Beylkin, Coifman, and Rokhlin 5]. They have been developed and thoroughly investigated in the We describe the wavelet algorithm and the theoretical results on its stability, convergence, and co...

A Fast Regularized Boundary Integral Method for Practical Acoustic Problems

To predict the sound field in an acoustic problem, the well-known non-uniqueness problem has to be solved. In a departure from the common approaches used in the prior literature, the weak-form of the Helmholtz differential equation, in conjunction with vector test-functions, is utilized as the basis, in order to directly derive non-hyper-singular boundary integral equations for the velocity pot...