A dual-level method of fundamental solutions for three-dimensional exterior high frequency acoustic problems

作者：Li, Junpu^*; Qin, Qinghua; Fu, Zhuojia

来源：Applied Mathematical Modelling, 2018, 63: 558-576.

DOI：10.1016/j.apm.2018.07.002

• Dual-level method of fundamental solutions
• Radial basis functions methods
• Helmholtz equation with large wavenumber
• Ill-conditioning
• Fictitious boundary

Physical essence of the fictitious boundary of the method of fundamental solutions has been a mystery for a long time. In this study, we attempt to explain the reason why fictitious boundary has such a dramatic effect on numerical results. The influence law of the fictitious boundary on numerical results is revealed. Based on this understanding, a dual-level method of fundamental solutions with self-adaptive adjustment coefficients is proposed. The competitive attributes of the method are that it inherits the high numerical efficiency of the method of fundamental solutions, and it improves numerical stability significantly. The effect of the fictitious boundary on numerical results is eliminated by introducing the concept of equivalent slope. It should be noted that the dual-level method of fundamental solutions can simulate exterior high frequency acoustic problems under the lowest sampling frequency allowed by the Shannon's sampling theorem. Numerical experiment with up to non-dimensional wavenumber of 600 has successfully been conducted on a single laptop when one uses 100,000 degrees of freedom.

• 出版日期2018-11
• 单位河海大学