I will describe a comprehensive approach to the numerical solution of integral equations on planar domains with corners. Integral equation methods are efficient and robust techniques for solving boundary value problems for linear constant coefficient partial differential equations. Their advantages make them the method of choice for modelling many physical phenomena.
The approach I will describe has numerous advantages over existing
techniques, which are quite limited in their ability to handle domains with complicated geometry. Most importantly, no asymptotic estimates for the behavior of solutions
are required and high-accuracy solutions to large-scale
problems can be obtained rapidly.
This is joint work with Vladimir Rokhlin.
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