报告一题目:Fast boundary element methods with hierarchical matrices
报告一时间：2022年3月4日（周五）16:00-18:00（北京时间）
报告一地点：线上腾讯会议（ID: 864-395-429）
ZoomMeeting ID: 677 8648 4220Passcode: 534930 Link: https://uni-kiel.zoom.us/j/67786484220?pwd=NXAvMERsMGhkeS9ES0svSTR5RFh2QT09
报告二题目:Directional H²-matrix compression for Helmholtz problems
报告二时间：2022年3月7日（周一）16:00-18:00（北京时间）
报告二地点：线上腾讯会议（ID: 864-395-429）
Meeting ID: 684 3990 5274Passcode: 111057Link: https://uni-kiel.zoom.us/j/68439905274?pwd=eENqQUw0UDVNTHhJWTZzZStZZU5BQT09
报告人：Steffen Börm教授, Kiel University, Germany
主办单位：力学与材料学院固体力学研究所
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报告一简介：
Using a boundary integral formula, a partial differential equation can be reduced to a boundary integral equation in volume. But the resulting boundary integral operator is nonlocal and direct discretization leads to dense matrices that are too expensive to compute and store. This problem can be solved by decomposing the low-rank blocks of an approximate matrix. The resulting hierarchical matrix reduces the complexity from O(n²) to O(n k log n), where n is the number of surface elements and k is the parameter controlling the accuracy. With more complex H² -matrices, the complexity can even be reduced to O(n k). This report introduces the concepts of H- and H²- matrices, from basic techniques such as interpolation to more efficient hybrid schemes. Numerical experiments show that this boundary with millions of elements can be dispensed with at the expense of discretization accuracy.
报告二简介：
H² matrix oriented compression for Helmholtz problems.
The H² matrix method is used to solve the high frequency Helmholtz boundary integral equation. This problem can be solved by splitting the kernel functions into plane waves and smoothing functions. This approach goes up to a oriented H² -matrix, each cluster using multiple bases to reflect plane waves in multiple directions. The hybrid approximation scheme algorithm with algebraic real-time recompression allows us to efficiently deal with very large high-frequency problems.
报告人简介：
Steffen Börm is a Professor of Mathematics and Chair of Scientific Computing at Kiel University, Germany. He has published more than 40 papers in peer-reviewed journals and 2 monographs. His research interests are numerical linear algebra and high-performance computing, currently with an emphasis on the applications of H-matrix solvers for the Helmholtz equation and integral equations. He was the Associate Editor of SIAM Journal on Scientific Computing. He has organized several national and international workshops and mini-workshops on h-matrix solvers and analysis of high frequency wave propagation, and in particular since 2003 he has organized the annual Hierarchical Matrix Winter School. He is also one of the developers of the open-source packages HLib and H2Lib for hierarchical matrices and H²-matrices.