講座主題：A numerical scheme for the time-fractional diffusion equation by layer potentials with applications to inverse problems
專家姓名：王海兵
工作單位：東南大學(xué)
講座時(shí)間：2021年12月16日 14:50-15:50
講座地點(diǎn)：騰訊會議，會議ID：403792057
主辦單位：煙臺大學(xué)數(shù)學(xué)與信息科學(xué)學(xué)院
內(nèi)容摘要：
In this talk, we show a numerical scheme for solving an initial-boundary value problem for the time-fractional diffusion equation. By expressing the solution as a single-layer potential, the initial-boundary value problem is transformed into a boundary integral equation for the unknown density function. To numerically solving the resulting boundary integral equation, we develop a stable discretization scheme for layer potentials. First, we rewrite the layer potential operators as generalized Abel integral operators in time. Then, the asymptotic expansions of those kernels at the initial time are derived. Consequently, we establish a stable time discretization scheme. The spatial discretization is performed by a standard quadrature rule for boundary integrals of smooth functions. Finally, we present several numerical examples to show the efficiency and accuracy of the proposed numerical scheme. Applications to inverse problems will also be discussed.
主講人介紹：
王海兵，東南大學(xué)數(shù)學(xué)學(xué)院教授，博士研究生導(dǎo)師，主要從事數(shù)學(xué)物理反問題的研究。現(xiàn)任中國數(shù)學(xué)會計(jì)算數(shù)學(xué)分會常務(wù)理事。2012年獲得北海道大學(xué)和東南大學(xué)的理學(xué)博士學(xué)位。目前正主持一項(xiàng)國家自然科學(xué)基金面上項(xiàng)目，代表性成果發(fā)表在SIAM系列刊物，IP，JCP，JDE等國際知名刊物上。
