Year: 2015
Type: article
Abstract: We present and study a novel numerical algorithm to approximate the action of T β := L − β T^\beta :=L^{-\beta } where L L is a symmetric and positive definite unbounded operator on a Hilbert space H 0 H_0 . The numerical method is based on a representation formula for T − β T^{-\beta } in terms of Bochner integrals involving ( I + t 2 L ) − 1 (I+t^2L)^{-1} for t ∈ ( 0 , ∞ ) t\in (0,\infty ) . To develop an approximation to T β T^\beta , we introduce a finite element approximation L h L_h to L L and base our approximation to T β T^\beta on T h β := L h <mml
Source: Mathematics of Computation
Authors: Andrea Bonito, Joseph Pasciak
Institution: Texas A&M University
Language: English
Subfield: Computational Mechanics
Field: Engineering
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2075532512