報(bào)告承辦單位: 數(shù)學(xué)與統(tǒng)計(jì)學(xué)院
報(bào)告題目: Multirate partially explicit scheme for multiscale flow problems
報(bào)告內(nèi)容: For time-dependent problems with high-contrast multiscale coefficients, the time step size for explicit methods is affected by the magnitude of the coefficient parameter. With a suitable construction of multiscale space, one can achieve a stable temporal splitting scheme where the time step size is independent of the contrast. Consider the parabolic equation with heterogeneous diffusion parameter, the flow rates vary significantly in different regions due to the high-contrast features of the diffusivity. In this talk, we aim to introduce a multirate partially explicit splitting scheme to achieve efficient simulation with the desired accuracy. We first design multiscale subspaces to handle flow with different speeds. Then a multirate time stepping is introduced for the partially explicit scheme. The stability of the multirate methods is analyzed for the partially explicit scheme. Moreover, we derive local error estimators corresponding to the two components of the solutions and provide an upper bound of the errors. An adaptive local temporal refinement framework is then proposed to achieve higher computational efficiency.
報(bào)告人姓名: 王亞婷
報(bào)告人所在單位: 香港大學(xué)數(shù)學(xué)系
報(bào)告人職稱/職務(wù)及學(xué)術(shù)頭銜: 助理教授
報(bào)告時(shí)間: 2022年4月18日16:00－17:30
報(bào)告方式: 騰訊會(huì)議 497-385-175
報(bào)告人簡介: 王亞婷2018年獲Texas A&M University博士學(xué)位，2018-2021年，赴普渡大學(xué)開展博士后研究。主要從事多尺度模型降階和相關(guān)的深度學(xué)習(xí)問題。