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| Author(s): |
Gilberto Luis Valente
Total Authors: 1
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| Document type: | Doctoral Thesis |
| Press: | Campinas, SP. |
| Institution: | Universidade Estadual de Campinas (UNICAMP). Faculdade de Engenharia Mecânica |
| Defense date: | 2020-08-28 |
| Examining board members: |
Marco Lúcio Bittencourt;
Alvaro Luiz Gayoso de Azeredo Coutinho;
Marcilio Alves;
Philippe Remy Bernard Devloo;
Josué Labaki
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| Advisor: | Edson Borin; Marco Lúcio Bittencourt |
| Abstract | |
This work describes the implementation of a serial and parallel software architecture called \hpfem for the high-order finite element method (HO-FEM). The software was designed to facilitate reusability and ease of maintenance. The implementation is based on the object-oriented paradigm in C++. It is possible to use different polynomial approximation orders for the mesh elements. The use of meshes with non-uniform degree distribution allows increasing the polynomial order just in elements with higher gradients in the approximate solution. Efficient procedures to calculate element matrices allow significant gains in terms of processing time and memory. A local algorithm based on the least-squares method is presented to obtain the approximation coefficients. This algorithm requires the solution of a linear system of equations for each element and obtain the local approximation coefficients by the inversion of the element matrices. The global solution for the coefficients shared by two or more elements are obtained by a weighted average of the local solutions and element measures (length, area or volume). Results for non-uniform order distribution are presented for meshes of squares and hexahedra with the projection problem. Code profile is analyzed to quantify the gains in terms of memory and processing. Scalability results for hybrid parallelism with OpenMP and MPI presented good speedup, solving linear and non-linear transient analysis problems with explicit time integration. In addition, there were weak and strong scalability for the parallel model using optimized linear algebra libraries. Scalability and profiling were evaluated in the IBM Blue Gene/Q Mira computer running the projection local solver on 32768 computer nodes with up to 840 million degrees of freedom. The explicit local solver was run in the Kahuna cluster with HT Intel Xeon E5-2670 processors, located at CCES Unicamp. Performance analyzes of the parallel solver in this cluster were performed by running crankshaft meshes with up to $1,791$ million elements and $400$ million of degrees of freedom (AU) | |
| FAPESP's process: | 12/19922-2 - High Order Finite Element Method on the High Performance Hybrid Architecture Applied on Structural Mechanics. |
| Grantee: | Gilberto Luis Valente da Costa |
| Support Opportunities: | Scholarships in Brazil - Doctorate |