
PETGEM: A parallel code for 3D CSEM forward modeling using edge finite elements
We present the capabilities and results of the Parallel Edgebased Tool ...
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A Numerical Comparison of an Isogeometric and a Classical HigherOrder Approach to the Electric Field Integral Equation
In this paper, we advocate a novel splinebased isogeometric approach fo...
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Manufactured Solutions for the MethodofMoments Implementation of the ElectricField Integral Equation
Though the methodofmoments implementation of the electricfield integr...
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An OSRC Preconditioner for the EFIE
The Electric Field Integral Equation (EFIE) is a wellestablished tool t...
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CodeVerification Techniques for the MethodofMoments Implementation of the ElectricField Integral Equation
The methodofmoments implementation of the electricfield integral equa...
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Efficient Spectral Methods for QuasiEquilibrium Closure Approximations of Symmetric Problems on Unit Circle and Sphere
Quasiequilibrium approximation is a widely used closure approximation a...
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Trefftz Functions for Nonlocal Electrostatics
Electrostatic interactions in solvents play a major role in biophysical systems. There is a consensus in the literature that the dielectric response of aqueous solutions is nonlocal: polarization depends on the electric field not only at a given point but in the vicinity of that point as well. This is typically modeled via a convolution of the electric field with an appropriate integral kernel. A primary problem with nonlocal models is high computational cost. A secondary problem is restriction of convolution integrals to the solvent, as opposed to their evaluation over the whole space. The paper develops a computational tool alleviating the "curse of nonlocality" and helping to handle the integration correctly. This tool is Trefftz approximations, which tend to furnish much higher accuracy than traditional polynomial ones. In the paper, Trefftz approximations are developed for problems of nonlocal electrostatics, with the goal of numerically "localizing" the original nonlocal problem. This approach can be extended to nonlocal problems in other areas of computational mathematics, physics and engineering.
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