ProPHLEX—An hp-adaptive finite element kernel for solving coupled systems of partial differential equations in computational mechanics

Liszka, Tadeusz; Tworzydlo, W. W.; Bass, J. M.; Sharma, Sameer; Westermann, Tim; Yavari, B.

doi:10.1016/s0045-7825(97)00088-1

Cited by 12 publications

(6 citation statements)

References 15 publications

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“…Although residuals can be computed for each of the field quantities separately, a generalization of explicit estimators in a straightforward manner is not possible. Liszka et al (1997) suggest to use an implicit error estimator based on a generalization of Bank and Weiser (1985). An embedded pair of FEM solutions with different orders ( p þ 1) and mesh size (h/2) is used in Solin et al (2010a).…”

Section: Adaptation In Coupled Problemsmentioning

confidence: 99%

Adaptation in coupled problems

Vokas

Kasper

2010

COMPEL - The International Journal for Computation and Mathematics in Electrical and Electronic Engineering

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If you would like to write for this, or any other Emerald publication, then please use our Emerald for Authors service information about how to choose which publication to write for and submission guidelines are available for all. Please visit www.emeraldinsight.com/authors for more information. About Emerald www.emeraldinsight.comEmerald is a global publisher linking research and practice to the benefit of society. The company manages a portfolio of more than 290 journals and over 2,350 books and book series volumes, as well as providing an extensive range of online products and additional customer resources and services.Emerald is both COUNTER 4 and TRANSFER compliant. The organization is a partner of the Committee on Publication Ethics (COPE) and also works with Portico and the LOCKSS initiative for digital archive preservation.*Related content and download information correct at time of download. Adaptation in coupled problems Christos Vokas and Manfred KasperInstitute of Micro System Technology, Hamburg University of Technology, Hamburg, Germany Abstract Purpose -The purpose of this paper is to address the formulation, implementation, and adaptation of closely coupled multi-physics problems with h-and p-adaptive finite element methods. A general formulation is chosen allowing for coupled problems of various types. Adaptation algorithms for h-and p-refinement are given. Design/methodology/approach -A generic system of second-order differential equations is used, where the field of each individual problem is represented as an entry in the list of field variables. Specific problems are implemented by mapping material coefficients to the coefficients of the generic form. An example with four natures is investigated with close coupling between electric, mechanical and thermal fields. h-and p-refinement using a single mesh is considered, where the element order may differ for individual fields. Findings -In coupled problems, the error in each single field is affected by approximation properties of all other field quantities. In order to allow for optimal convergence order in the number of degrees of freedom, the error contributions of all fields have to be considered. Separate error estimation in each field is needed especially in h-adaptation on a single mesh. Energy coupling coefficients were introduced to derive an adaptation criterion. Convergence analysis of h-and p-adaptation proves the feasibility of the approach. Originality/value -Piezopyroelectricity considers thermal effects in high-frequency piezoelectric materials, which is a coupled problem of four natures. The paper introduces an adaptation criterion for such complicated coupled problems and proves feasibility.

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Section: Adaptation In Coupled Problemsmentioning

confidence: 99%

Adaptation in coupled problems

Vokas

Kasper

2010

COMPEL - The International Journal for Computation and Mathematics in Electrical and Electronic Engineering

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“…Although the writing of complex equations as systems of purely real equations may seem somewhat awkward to the reader, the reason motivating this choice in the present paper is that the ProPHLEX FE development library and kernel used by the authors requires all quantities to be purely real (see [1]). …”

Section: Theorymentioning

confidence: 99%

“…The basis functions, which in the present case are the hierarchic polynomials defined in [1], are grouped into the matrix…”

Section: Finite Element Equationsmentioning

confidence: 99%

“…The basic building block for the tool is a state-of-the-art commercial finite element kernel and library called ProPHLEX, which is developed at COMCO/Altair Engineering (see [1]). FESTA is capable of computing efficiently the multistatic scattered field in the vicinity of localized inhomogeneities and/or of elastic objects with internal structure, such as mines.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A Finite-Element Tool for Scattering from Localized Inhomogeneities and Submerged Elastic Structures

Zampolli¹,

Burnett²,

Jensen³

et al. 2004

AIP Conference Proceedings

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A steady-state 3-D finite-element tool called FESTA (Finite-Element STructural Acoustics), is being developed at the NATO Undersea Research Centre. The code is geared towards a variety of applications in underwater acoustics, such as multistatic scattering from localized inhomogeneities, scattering across interfaces between fluids and/or solids, and multistatic scattering from single and multiple fluid-loaded elastic targets. The hp-adaptive finite-element technology used to develop FESTA allows the user to optimize the convergence as well as the demand on computing resources by selectively changing the element size (h-refinement) and/or by increasing the order of the polynomial finite-element shape functions (p-enrichment). An efficient hybrid tool for the computation of multistatic scattering from targets buried, partially buried or proud inside shallow water waveguides is being developed in conjunction with MIT. In this hybrid tool FESTA is used to perform target computations in the near field of the scatterer, while the waveguide propagation model OASES computes the far field propagation of the incident and scattered acoustic fields. The presentation focuses on the most relevant details of the formulations implemented in FESTA, as well as on application examples for frequencies ranging from 1 kHz to a few tens of kHz.

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“…This kernel is being linked as a library into PHLEXcrack™. PHLEXcrack code is based on a proprietary FEM environment ProPHLEX, which was during this project, expanded to handle the EPM and CEPM methods [19]. …”

Section: Introductionmentioning

confidence: 99%