Unified hybrid-trefftz finite element formulation for dynamic problems

Ionuţ Dragoş Moldovan, Ildi Cismaşiu, João António Teixeira de Freitas

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review

Abstract

Hybrid-Trefftz finite elements combine favourable features of the Finite and Boundary Element methods. The domain of the problem is divided into finite elements, where the unknown quantities are approximated using bases that satisfy exactly the homogeneous form of the governing differential equation. The enforcement of the governing equations leads to sparse and Hermitian solving systems (as typical to Finite Element Method), with coefficients defined by boundary integrals (as typical to Boundary Element Method). Moreover, the physical information contained in the approximation bases renders hybrid-Trefftz elements insensitive to gross mesh distortion, nearly-incompressible materials, high frequency oscillations and large solution gradients. A unified formulation of hybrid-Trefftz finite elements for dynamic problems is presented in this chapter. The formulation reduces all types of dynamic problems to formally identical series of spectral equations, regardless of their nature (parabolic or hyperbolic) and method of time discretization (Fourier series, time-stepping procedures, or weighted residual methods). For non-homogeneous problems, two novel methods for approximating the particular solution are presented. The unified formulation supports the implementation of hybrid-Trefftz finite elements for a wide range of physical applications in the same computational framework.

Original languageEnglish
Title of host publicationAdvances in Trefftz Methods and Their Applications
EditorsC. Alves, A. Karageorghis, V. Leitão, S. Valtchev
Place of PublicationCham
PublisherSpringer
Pages157-188
Number of pages32
ISBN (Electronic)978-3-030-52804-1
ISBN (Print)978-3-030-52803-4
DOIs
Publication statusPublished - 2020

Publication series

NameSEMA SIMAI Springer Series
PublisherSpringer
Volume23
ISSN (Print)2199-3041
ISSN (Electronic)2199-305X

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