1. Get familiar with the fundamental theories about the Finite Element Methods and its typical application;

2. Gain a comprehensive perspective throughout FPGA based matrix equation solution arithmetic;

3. Design software simulation and hardware solution using parallel technique for simple finite element.

The parallel technique was used in the Discrete Element Position Calculation block. Each sub-block only response for the points within the area given by the Equation Matrix Solution block and defined by the given Finite Element model.

## Reference

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[3] K. D. Underwood and K. S. Hemmert, "Closing the gap: CPU and FPGA trends in sustainable floating-point BLAS performance," in *Field-Programmable Custom Computing Machines, 2004. FCCM 2004. 12th Annual IEEE Symposium on*, 2004, pp. 219-228.

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[8] G. Altaf Abdul, L. Wayne, Y. K. C. Peter, S. Nabeel, and H. James, "Automating Customisation of Floating-Point Designs," in *Proceedings of the Reconfigurable Computing Is Going Mainstream, 12th International Conference on Field-Programmable Logic and Applications*: Springer-Verlag, 2002.

[9] L. Jian, T. Russell, and M. Oskar, "Floating Point Unit Generation and Evaluation for FPGAs," in *Proceedings of the 11th Annual IEEE Symposium on Field-Programmable Custom Computing Machines*: IEEE Computer Society, 2003.

[10] M. P. Leong, M. Y. Yeung, C. K. Yeung, C. W. Fu, P. A. Heng, and P. H. W. Leong, "Automatic Floating to Fixed Point Translation and its Application to Post-Rendering 3D Warping," in *Proceedings of the Seventh Annual IEEE Symposium on Field-Programmable Custom Computing Machines*: IEEE Computer Society, 1999.

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[13] L. Zhuo and V. K. Prasanna, "Design tradeoffs for BLAS operations on reconfigurable hardware," in *Parallel Processing, 2005. ICPP 2005. International Conference on*, 2005, pp. 78-86.

[14] R. M. Gerald and K. P. Viktor, "An FPGA-Based Floating-Point Jacobi Iterative Solver," 2005, p. 420.

[15] M. Fischborn, P. Kuo-Peng, N. Sadoswki, J. P. A. Bastos, and J. A. T. J. Trevisan, "LU Parallel Preconditioning with Block Intersection Applied to FEM on Computer Clusters," in *Electromagnetic Field Computation, 2006 12th Biennial IEEE Conference on*, 2006, pp. 404-404.

[16] K. J. Paar, P. M. Athanas, and C. M. Edwards, "Implementation of a finite difference method on a custom computing platform," in *High-Speed Computing, Digital Signal Processing, and Filtering Using reconfigurable Logic, Proc. SPIE 2914*, 1996, pp. 44-53.

[17] E. Motuk, E. Motuk, R. Woods, and S. Bilbao, "Implementation of finite difference schemes for the wave equation on FPGA

Implementation of finite difference schemes for the wave equation on FPGA," in *Acoustics, Speech, and Signal Processing, 2005. Proceedings. (ICASSP '05). IEEE International Conference on*, 2005, pp. iii/237-iii/240 Vol. 3.

## Appendix

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