An object-oriented approach for parallel two- and three-dimensional adaptive finite element computations |
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| Affiliation: | 1. Department of Mechanics and Aerospace Engineering, Southern University of Science and Technology, Shenzhen 518055, PR China;2. School of Mechanical and Manufacturing Engineering, University of New South Wales, Sydney, New South Wales 2052, Australia;3. School of Mechanical Engineering, The University of Adelaide, Adelaide, South Australia 5005, Australia;1. National Institute of Neurological Disorders and Stroke, National Institutes of Health, Bethesda, MD;2. Biostatistics Center, The George Washington University, Washington, DC;3. Department of Diagnostic Imaging and Radiology, Children''s National Medical Center, Washington, DC;4. Section of Pediatric Radiology, University of Michigan, Ann Arbor, MI;5. Division of Radiology, Arkansas Children''s Hospital, Little Rock, AR;6. Department of Obstetrics and Gynecology, University of Alabama at Birmingham, Birmingham, AL;7. Department of Obstetrics and Gynecology, Case Western Reserve University-MetroHealth Medical Center, Cleveland, OH, and University of Tennessee, Memphis, TN;8. Department of Obstetrics and Gynecology, University of Utah Health Sciences Center, Salt Lake City, UT;10. Department of Obstetrics and Gynecology, The Ohio State University, Columbus, OH;11. Department of Obstetrics and Gynecology, Thomas Jefferson University and Drexel University, Philadelphia, PA;12. Department of Obstetrics and Gynecology, Wayne State University, Detroit, MI;13. Department of Obstetrics and Gynecology, University of North Carolina at Chapel Hill, Chapel Hill, NC;14. Department of Obstetrics and Gynecology, University of Texas Health Science Center at Houston-Children''s Memorial Hermann Hospital, Houston, TX;15. Department of Obstetrics and Gynecology, Columbia University, New York, NY;16. Department of Obstetrics and Gynecology, Brown University, Providence, RI;17. Department of Obstetrics and Gynecology, University of Miami, Miami, FL;18. Department of Obstetrics and Gynecology, Northwestern University, Chicago, IL;19. Department of Obstetrics and Gynecology, University of Texas Medical Branch, Galveston, TX;20. Department of Obstetrics and Gynecology, University of Texas at San Antonio, San Antonio, TX;21. Department of Obstetrics and Gynecology, University of Pittsburgh, Pittsburgh, PA |
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| Abstract: | For the mathematically sound, cost effective, flexible and automatic computation of structural mechanical problems with error tolerances, adaptive finite element meshes (h-adaptivity) and elements with different Ansatz order (p-adaptivity) and dimension (d-adaptivity) are desirable. Furthermore, because of the numerical effort, the use of parallel computers is adequate. Object-oriented data structures and algorithms are presented which support these adaptive formulations. In this paper, we describe a refinement algorithm which adapts hexahedral meshes in a node regular way, i.e. without hanging nodes. Moreover, classes implementing the mathematical operators and structures arising in the finite element formulation are introduced within the object oriented concept. They offer the means to implement FE formulations in a way, very similar to the mathematical notation. For these purposes, an object-oriented language is strongly required in order to get a general and simple program structure, even for highly complex tasks with h-, p- and d-adaptivity and distributed data. |
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