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DOE OSTI · 1765762

A Fast Solver for the Fractional Helmholtz Equation

Glusa, Christian Alexander·Antil, Harbir·D'Elia, Marta·van Bloemen Waanders, Bart G.·Weiss, Chester Joseph
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Abstract

The purpose of this paper is to study a Helmholtz problem with a spectral fractional Laplacian, instead of the standard Laplacian. Recently, it has been established that such a fractional Helmholtz problem better captures the underlying behavior in Geophysical Electromagnetics. In this work, we establish the well-posedness and regularity of this problem. We introduce a hybrid spectral-finite element approach to discretize it and show well-posedness of the discrete system. In addition, we derive a priori discretization error estimates. Finally, we introduce an efficient solver that scales aswell as the best possible solver for the classical integer-order Helmholtz equation. We conclude withseveral illustrative examples that confirm our theoretical findings.

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97 MATHEMATICS AND COMPUTINGFractional Helmholtz equationerror analysisspectral fractional Laplacian

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Glusa, Christian Alexander, Antil, Harbir, D'Elia, Marta, van Bloemen Waanders, Bart G., Weiss, Chester Joseph. 2021-04-26. A Fast Solver for the Fractional Helmholtz Equation. https://doi.org/10.1137/19m1302351

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