Fictitious Domain Approach for Spectral/hp Element Method
L. Parussini

Source CMES: Computer Modeling in Engineering & Sciences, Vol. 17, No. 2, pp. 95-114, 2007
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Keywords fictitious domain, Lagrange multipliers, spectral/hp element method, Poisson problem.
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 \Omega to be solved on a simpler domain \Pi containing \Omega. The Poisson equation, extended to the new domain \Pi , 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 \eta 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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