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FAST MULTIPOLE BOUNDARY ELEMENT METHOD FOR SOLVING TWO-DIMENSIONAL ACOUSTIC WAVE PROBLEMS

BAPAT, MILIND SHRIKANT
http://rave.ohiolink.edu/etdc/view?acc_num=ucin1163773308

Abstract Details

2006, MS, University of Cincinnati, Engineering : Mechanical Engineering.
The boundary element method (BEM) is a numerical method for solving boundary value problems. The boundary element method has a clear advantage over other techniques like finite element method (FEM) in problems involving infinite domains. Hence the boundary element method has found many applications in the field of acoustics which often exist in infinite domains. The traditional approach for finding solutions to acoustic problems using the boundary element method has a computational complexity of the order O(N 2). This makes the computation very slow as the number of nodes increase. A new technique called fast multipole method (FMM) has emerged in the last decade. Replacing the normal matrix-vector multiplication with the fast multipole method reduces the computational time to order O(N). In this thesis the fast multipole method has been used to accelerate the boundary element method for 2-D acoustic wave problems. The relevant formulae are derived. It is shown that the computational time is of the order O(N) for this formulation. It is also observed that the memory required is much lesser and hence larger models can be solved. The formulation is a very basic one and gives good results as shown by the numerical examples. Use of higher-order elements and hypersingular formulation will result in a very capable and robust solver in the future.
Dr. Yijun Liu (Advisor)
85 p.
Engineering, Mechanical
Fast multipole method

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Citations

  • BAPAT, M. S. (2006). FAST MULTIPOLE BOUNDARY ELEMENT METHOD FOR SOLVING TWO-DIMENSIONAL ACOUSTIC WAVE PROBLEMS [Master's thesis, University of Cincinnati]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1163773308

    APA Style (7th edition)

  • BAPAT, MILIND. FAST MULTIPOLE BOUNDARY ELEMENT METHOD FOR SOLVING TWO-DIMENSIONAL ACOUSTIC WAVE PROBLEMS. 2006. University of Cincinnati, Master's thesis. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=ucin1163773308.

    MLA Style (8th edition)

  • BAPAT, MILIND. "FAST MULTIPOLE BOUNDARY ELEMENT METHOD FOR SOLVING TWO-DIMENSIONAL ACOUSTIC WAVE PROBLEMS." Master's thesis, University of Cincinnati, 2006. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1163773308

    Chicago Manual of Style (17th edition)

ucin1163773308
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© 2006, all rights reserved.
This open access ETD is published by University of Cincinnati and OhioLINK.