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The high-order scheme is based on boundary integral equations, and achieves many digits of accuracy with ease.
Methods based on boundary integral equations are natural in this context, since they discretize the interface alone and can achieve high order accuracy in complicated geometries.
Based on boundary integral equations, our method splits the inverse problem into a well-posed direct problem followed by a smaller ill-posed problem which has advantages both in understanding the inverse problem and in the numerical reconstructions.
For optical waveguides with high index-contrast and sharp corners, existing full-vectorial mode solvers including those based on boundary integral equations typically have only second or third order of accuracy.
A recently developed method (the so-called BIE-NtD method) based on boundary integral equations (BIEs) and Neumann-to-Dirichlet (NtD) maps achieves high order of accuracy for dielectric waveguides.
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This representation is very useful for numerical methods which are based on boundary-integral formulations such as boundary-element method since the numerically evaluated part is not responsible for the singularity.
Numerical studies are based on boundary-integral methods for crystals consisting of multiple scatterers.
It is based on boundary-integral representations of the electromagnetic fields.
An exact non-reflecting boundary conditions based on a boundary integral equation or a modified Kirchhoff-type formula is derived for exterior three-dimensional wave equations.
In many analyses of engineering problems based on boundary element methods, a large number of regular and/or singular domain integrals must be accurately evaluated over a single domain.
An accurate computational method based on the boundary integral formulation is presented for solving boundary value problems for Stokes and Darcy flows.
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