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...

Abstract This expository paper is concerned with the direct integral formulations for boundary value problems of the Helmholtz equation. We discuss unique solvability for the corresponding boundary integral equations and its relations to the interior eigenvalue value problems of the Laplacian. Based on the integral representations, we study the asymptotic behaviors of the solutions to the bound...

The main subject of this contribution is to present some recent methods, specially designed to be implemented on parallel platforms, to deal with acoustic scattering problems involving a bounded zone filled by a heterogeneous medium. The main approach is to couple a Finite Element Method, for handling this zone, with a Boundary Integral Equation, specially adapted to treat the unbounded part of...

In this article we review recent progress on the design, analysis and implementation of numerical-asymptotic boundary integral methods for the computation of frequencydomain acoustic scattering in a homogeneous unbounded medium by a bounded obstacle. The main aim of the methods is to allow computation of scattering at arbitrarily high frequency with finite computational resources.

Boundary Integral Methods for Multicomponent Fluids and Multiphase Materials T. Y. Hou,∗ J. S. Lowengrub,† and M. J. Shelley‡ ∗Department of Applied Mathematics, California Institute of Technology, Pasadena, California 91125; †School of Mathematics, University of Minnesota, Minneapolis, Minnesota 55455; and Department of Mathematics, University of North Carolina, North Carolina 27599; and ‡Cour...

In this paper, the boundary-based estimation of pressure distribution in the cardiovascular system is investigated using two dimensional flow images. The conventional methods of non-invasive estimation of pressure distribution in the cardiovascular flow domain use the differential form of governing equations. This study evaluates the advantages of using the integral form of the equations in the...

Domain decomposition methods are designed to deal with coupled or transmission problems for partial differential equations. Since the original boundary value problem is replaced by local problems in substructures, domain decomposition methods are well suited for both parallelization and coupling of different discretization schemes. In general, the coupled problem is reduced to the Schur complem...

In this paper, the boundary-based estimation of pressure distribution in the cardiovascular system is investigated using two dimensional flow images. The conventional methods of non-invasive estimation of pressure distribution in the cardiovascular flow domain use the differential form of governing equations. This study evaluates the advantages of using the integral form of the equations in the...