Approximation of higher-order powers of the spectral fractional Laplacian via polyharmonic extension

TL;DR

This paper introduces a numerical method based on polyharmonic extension to approximate higher-order spectral fractional Laplacians, enabling more accurate discretization for fractional powers between 1 and 2.

Contribution

The paper presents a novel polyharmonic extension approach for discretizing higher-order spectral fractional Laplacians, expanding computational tools for fractional PDEs.

Findings

Developed a new numerical discretization technique for $(-igtriangleup)^s$ with $s ext{ in } (1,2)$.

Demonstrated improved accuracy over existing methods for fractional Laplacian approximation.

Applicable to complex boundary value problems involving higher-order fractional operators.

Abstract

We use the polyharmonic extension approach to develop a numerical technique for discretizing higher-order powers of the spectral fractional Laplacian $(-\Delta)^s$ with $s \in (1,2)$.