|
Paradox, Paradise and Parasite of the BEM/BIEM
Jeng-Tzong Chen, National Taiwan Ocean University Chair: Chia-Ming Fan Time: 2019/12/18 13:20-14:00 (102, 1F, TICC) |
Abstract:
It is well known that BEM/BIEM is an acceptable approach for solving engineering problems. It is a paradise in several aspects, one-dimension reduction of mesh, infinite domain, stress concentration and crack problems. Several successful experiences in Taiwan will be demonstrated. However, it also results in paradox and parasites in some cases. Rank-deficient matrix appears due to the degenerate scale, degenerate boundary, spurious eigenvalue and fictitious frequency once the BIEM/BEM is used for solving boundary value problems. Based on the well-posed dual formulation of the BEM/BIEM, full rank promotion can be achieved. In this talk, three parts will be given. First, the TwSIAM will be introduced. Second, the history of Taiwan BEM development will be addressed. Third, the rank-deficiency system in the BIEM/BEM will be reviewed and transformed to the well-posed system. Finally, I will mention recent works of NTOU/MSV group on the quaternion and the Clifford BEM.
It is well known that BEM/BIEM is an acceptable approach for solving engineering problems. It is a paradise in several aspects, one-dimension reduction of mesh, infinite domain, stress concentration and crack problems. Several successful experiences in Taiwan will be demonstrated. However, it also results in paradox and parasites in some cases. Rank-deficient matrix appears due to the degenerate scale, degenerate boundary, spurious eigenvalue and fictitious frequency once the BIEM/BEM is used for solving boundary value problems. Based on the well-posed dual formulation of the BEM/BIEM, full rank promotion can be achieved. In this talk, three parts will be given. First, the TwSIAM will be introduced. Second, the history of Taiwan BEM development will be addressed. Third, the rank-deficiency system in the BIEM/BEM will be reviewed and transformed to the well-posed system. Finally, I will mention recent works of NTOU/MSV group on the quaternion and the Clifford BEM.
