Haijun Wu (Shanghai Jiao Tong University, China) - Séminaire du LVA

Fast multipole boundary element method for acoustic problems and its applications

Boundary element method (BEM), a numerical method based on integral equation, can reduce the dimension of the model, and only requires the boundary to be discretized. It is easy to handle the far field boundary condition with the BEM since the integral equation automatically satisfies the radiation condition. Although dimension is reduced, the coefficient matrix generated by the BEM is full, non-symmetrical and even singular, which results in huge memory cost and computational complexity. Those features prevent BEM from the analyses of large scale acoustic problems. Currently, the analyses and studies for acoustic problems tend to large scale and multi-physics models, such as simulations for scattering and radiation of submarine, taking off and landing noise of airplane, acoustic characteristics of organs and tissues and the optimization of coupled structure-acoustics. Those models will generate DOFs at the level of hundreds of thousands or even several millions and thus urgently demand the BEM can solve such large scale acoustic problems within reasonable time. The fast multipole method (FMM) can reduce the memory and improve the computational efficiency dramatically. It presents a potential way to solve the large scale acoustic problems.

The present talk introduces the recent development BEM in our group for free space, multi-domain and half space acoustic problems based on the FMM. New theories and algorithms were proposed to solve the two bottlenecks, large memory and huge computational complexity, of BEM. The FMBEM were applied to predict the acoustic radiation and structure-acoustic optimization for large scale engineering problems. Those successful applications demonstrated the super computational capability of the FMBEM for large scale acoustic problems and the potential in the acoustic optimization.

Speaker Biography: Dr. Haijun Wu is an assistant professor in the School of Mechanical Engineering (ME), Shanghai Jiao Tong University (SJTU). He obtained his PhD degree at Shanghai Jiao Tong University in 2013. Prior to join the ME department, he conducted two years of joint-postdoc research, one year at SJTU and one year at Hon Kong University of Science and Technology. His current research interests include High Performance Computing of Structure, Fluid and Acoustics; Advanced Theory of Acoustic Radiation Modes and its Applications; Acoustic Inverse Problems and its Applications; Isogeometric Analysis.

Reference
[1] Haijun Wu, Weikang Jiang,Haibin Zhang. A mapping relationship based near-field acoustic holography with spherical fundamental solutions for Helmholtz equation[J]. Journal of Sound & Vibration, 2016, 373:66-88.
[2] Haijun Wu, Wenjing Ye, Weikang Jiang, Isogeometric finite element analysis of interior acoustic problems, Applied Acoustics, doi:10.1016/j.apacoust.2015.07.002
[3] Haijun Wu, Weikang Jiang, Yilin Zhang, Wenbo Lu, A method to compute the sound power based on mapped acoustic radiation modes, The Journal of the Acoustical Society of America, 135(2), 679-692, 2014.
[4] Haijun Wu, Yijun Liu, Weikang Jiang, A fast multipole boundary element method for three-dimensional half-space acoustic wave problems over an impedance plane, International Journal of Computational Methods, 12(1), 1350090-25, 2015.
[5] Haijun Wu, Weikang Jiang, Yijun Liu, Analyzing Acoustic Radiation Modes of Baffled Plates with A Fast Multipole Boundary Element Method," ASME: Journal of vibration and acoustics, 135(1), 011007-7, 2013.
[6] Haijun Wu, Yijun Liu, Weikang Jiang, A low frequency fast multipole boundary element method based on analytical integration of the hypersingular integral for 3D acoustic problems, Engineering Analysis with Boundary Elements, 37(2), 309-318, 2012.
[7] Haijun Wu, Yijun Liu, Weikang Jiang, A fast multipole boundary element method for 3D multi-domain acoustic scattering problems based on the Burton-Miller formulation, Engineering Analysis with Boundary Elements, 36(5), 779-788, 2012.
[8] Haijun Wu, Yijun Liu, Weikang Jiang, Analytical integration of the moments in the diagonal form fast multipole boundary element method for 3-D acoustic wave problems, Engineering Analysis with Boundary Elements, 36(2), 248-254, 2012.
[9] Haijun Wu, Weikang Jiang, Yijun Liu, Diagonal form fast multipole boundary element method for 2D acoustic problems based on Burton-Miller boundary integral equation formulation and its applications, Applied Mathematics and Mechanics, 32(8), 981-996, 2011.
[10] Haijun Wu, Weikang Jiang, Wenbo Lu, Analytical moment expression for linear element in diagonal form fast multipole boundary element method, Journal of Mechanical Science and Technology, 25(7), 1711-1715, 2011.