2017年08月17日 |  English version
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An augmented ADI Method for heat equations with an interface

报告题目:An augmented ADI Method for heat equations with an interface

报告人:Professor Zhilin Li,North Carolina State University

报告时间:2017年6月20日(周二)9:30

报告地点:行健楼学术报告室526

摘要:A new second-order accurate ADI (alternating direction implicit) method for heat equations with a piece-wise constant but discontinuous coefficient and a singular source along an arbitrary but fixed interface has been developed. In the literature, an earlier ADI method by Z. Li & A. Mayo for heat equations with an interface assuming constant coefficient was developed. While the ADI method developed by S. Zhao in JSC for interface problems works for discontinuous coefficients but seems to be only first order accurate in time and the resulting linear system of equation is pentadiagonal instead of tridiagonal in the original ADI method.  Two novel new ideas make the new ADI working possible. The first idea is to reformulate, or preconditioning the partial differential equation so that the discontinuous coefficient is not involved in the highest derivative term. The second idea is to introduce an augmented variable along the interface to get the dimension-by-dimension jump conditions needed to get accurate discretization in coordinate direction.

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