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Starting with my PhD, I developed an interest in fast solution methods for integral equations such as the Fast Multipole Method (FMM), methods based on Hierarchical Matrices, methods based on wavelets and asymptotic methods, with a particular view on their application for acoustic and electromagnetic wave scattering and wave propagation simulations.
One of the challenges left in the field of numerical integration is the evaluation of highly oscillatory integrals. Although this is often considered to be a resource-intensive problem, in many cases the exact opposite is true. From a computational point of view, one might conclude that it is actually cheaper to evaluate highly oscillatory integrals than non-oscillatory ones. The benefits increase both with increasing frequency and with increasing number of dimensions.
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Yiqing Zhou,Daan Huybrechs
Journal of Computational and Applied Mathematics (2024): 115870
arxiv(2023)
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J. Comput. Appl. Math. (2023): 115317-115317
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CoRR (2023)
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arxiv(2023)
SIAM JOURNAL ON NUMERICAL ANALYSISno. 6 (2023): 2580-2600
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