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Fast Finite Element Method Using Multi-Step Mesh Process | ||
| AUT Journal of Electrical Engineering | ||
| مقاله 2، دوره 45، شماره 2، بهمن 2013، صفحه 1-9 اصل مقاله (751.82 K) | ||
| نوع مقاله: Research Article | ||
| شناسه دیجیتال (DOI): 10.22060/eej.2013.430 | ||
| نویسندگان | ||
| M. Badiei Khuzani1؛ Gh. Moradi* 2 | ||
| 1PhD. Student, School of Engineering and Applied Sciences, Harvard University, Cambridge, United State | ||
| 2Assistant Professor, Department of Electrical Engineering, Amirkabir University of Technology, Tehran, Iran | ||
| چکیده | ||
| This paper introduces a new method for accelerating current sluggish FEM and improving memory demand in FEM problems with high node resolution or bulky structures. Like most of the numerical methods, FEM results to a matrix equation which normally has huge dimension. Breaking the main matrix equation into several smaller size matrices, the solving procedure can be accelerated. For implementing this matter, the meshing process should be changed. Here, a multi-step meshing process is proposed which consists of both posterior and main levels. The posterior level is used for separating matrix equations from each other and the main level for field computation in the problem. The proposed approach is compatible with other optimizing method for increasing speed in FEM. Therefore, combining this method with other methods creates a powerful asset for solving complex FEM problems. The results show that the proposed method speeds up FEM and decreases the memory capacity. In addition, it brings the facility of parallel computation which is of great importance in fast computational algorithm | ||
| کلیدواژه‌ها | ||
| finite element method؛ Multi-Step Mesh Process؛ Parallel Computation؛ Adaptive Mesh Refinement | ||
| عنوان مقاله [English] | ||
| Fast Finite Element Method Using Multi-Step Mesh Process | ||
| نویسندگان [English] | ||
| M. Badiei Khuzani1؛ Gh. Moradi2 | ||
| 1PhD. Student, School of Engineering and Applied Sciences, Harvard University, Cambridge, United State | ||
| 2Assistant Professor, Department of Electrical Engineering, Amirkabir University of Technology, Tehran, Iran | ||
| چکیده [English] | ||
| This paper introduces a new method for accelerating current sluggish FEM and improving memory demand in FEM problems with high node resolution or bulky structures. Like most of the numerical methods, FEM results to a matrix equation which normally has huge dimension. Breaking the main matrix equation into several smaller size matrices, the solving procedure can be accelerated. For implementing this matter, the meshing process should be changed. Here, a multi-step meshing process is proposed which consists of both posterior and main levels. The posterior level is used for separating matrix equations from each other and the main level for field computation in the problem. The proposed approach is compatible with other optimizing method for increasing speed in FEM. Therefore, combining this method with other methods creates a powerful asset for solving complex FEM problems. The results show that the proposed method speeds up FEM and decreases the memory capacity. In addition, it brings the facility of parallel computation which is of great importance in fast computational algorithm | ||
| کلیدواژه‌ها [English] | ||
| finite element method, Multi-Step Mesh Process, Parallel Computation, Adaptive Mesh Refinement | ||
| مراجع | ||
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[1] Yee Hui Lee and Yilong Lu, “Accelerating Numerical Electromagnetic Code Computation By Using the Wavelet transform”, IEEE Trans on MTT, vol. 34, no. 5, 1998. [2] Thomas Grätsch, Klaus-Jürgen Bathe, “A Posteriori Error Estimation Techniques in Practical Finite Element analysis”, Elsevier, Computer and structure, 2004. [3] Babuška I, Chandra J, Flaherty J.E. “Adaptive Computational Methods for Partial Differential Equations”, Society for Industrial and Applied Mathematics, Philadelphia, 1983. [4] Babuška I, Zienkiewicz O.C, Gago J, Oliveira E.R, “Accuracy Estimates and Adaptive Refinements in Finite Element Computation”, New York: John Wiley and Sons, 1986 [5] Haixin Liu and Dan Jiao, “A Direct Finite-Element-Based Solver of Significantly Reduced Complexity for Solving Large-Scale Electromagnetic Problems,” Microwave Symposium Digest. MTT '09. IEEE MTT-S, pp. 177, 2009. [6] Susanne C. Brenner and L. Ridgway Scott, “The Mathematical Theory of Finite Element Methods”, 2nd edition. New York: Springer-Verlag, 2002, pp. 1-3. [7] Ainsworth M, Oden J.T, “A Posterior Error Estimation in Finite Element Analysis”, New York: John Wiley and Sons, 2000. [8] Anastasis C. Polycarpou, “Introduction to the Finite Element Method in Electromagnetics”, 1st edition. California Morgan &.Claypool Publishers’ series, 2006, pp. 93-94. [9] Jianming Jin, “The Finite Element Method in Electromagnetic”, New York: IEEE Press, 2002. | ||
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