Journal
JOURNAL OF SCIENTIFIC COMPUTING
Volume 49, Issue 3, Pages 351-366Publisher
SPRINGER/PLENUM PUBLISHERS
DOI: 10.1007/s10915-011-9468-4
Keywords
Tailored finite point method; Wave equation; Conservation laws; High frequency; Discontinuity
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Funding
- NSFC [11071139]
- National Basic Research Program of China [2011CB309705]
- Tsinghua University
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Following the idea of the tailored finite point method proposed in Han and Huang (J. Comput. Math. 26:728-739, 2008) and Huang (Netw. Heterog. Media 4:91-106, 2009), a series of efficient numerical schemes are developed for the one dimensional scalar wave equation within various types of media. Stability and accuracy are analyzed and numerically verified. In particular we can obtain unconditionally stable implicit schemes that can be solved explicitly for boundary value problems. We can also deal with the propagation of discontinuity and highly oscillatory waves efficiently. The generalization to higher order schemes is straightforward.
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