Open Access

ARTICLE

Fictitious Domain Approach for Spectral/hp Element Method

L. Parussini ¹

1 University of Trieste, Mech. Eng. Dept., ITALY

Computer Modeling in Engineering & Sciences 2007, 17(2), 95-114. https://doi.org/10.3970/cmes.2007.017.095

Abstract

We propose a fictitious domain method combined with spectral/hp elements for the solution of second-order differential problems. This paper presents the formulation, validation and application of fictitiuos domain-spectral/hp element algorithm to one- and two-dimensional Poisson problems. Fictitious domain methods allow problems formulated on an intricate domain Ω to be solved on a simpler domain Π containing Ω. The Poisson equation, extended to the new domain Π, is expressed as an equivalent set of first-order equations by introducing the gradient as an additional indipendent variable, and spectral/hp element method is used to develop the discrete model. Convergence of relative energy norm η is verified computing smooth solutions to one- and two-dimensional Poisson equations. Thermal field calculations for heatsink profile is presented to demonstrate the predictive capability of the proposed formulation.

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