主講人：李會(huì)元 中國(guó)科學(xué)院軟件研究所研究員

時(shí)間：2023年5月12日15：00

地點(diǎn)：三號(hào)樓301室

舉辦單位：數(shù)理學(xué)院

主講人介紹：李會(huì)元，中國(guó)科學(xué)院軟件研究所研究員，博士生導(dǎo)師。主要從高性能軟件與算法、偏微分方程譜與譜元方法等研究工作；任中國(guó)數(shù)學(xué)會(huì)理事，曾任北京計(jì)算數(shù)學(xué)會(huì)理事、中國(guó)仿真學(xué)會(huì)青年委員會(huì)理事。先后訪(fǎng)問(wèn)美國(guó)普渡大學(xué)、俄勒岡大學(xué)、南卡來(lái)羅納大學(xué)，新加坡南洋理工大學(xué)，香港城市大學(xué)。主持國(guó)家自然科學(xué)基金項(xiàng)目6項(xiàng)目，參與國(guó)家自然科學(xué)基金委重點(diǎn)項(xiàng)目3項(xiàng)；參與國(guó)家重點(diǎn)研發(fā)計(jì)劃高性能計(jì)算專(zhuān)項(xiàng)、任課題負(fù)責(zé)人；參與中國(guó)科學(xué)院戰(zhàn)略性先導(dǎo)科技專(zhuān)項(xiàng)。在非規(guī)則區(qū)域傅里葉分析與正交多項(xiàng)式、奇性薛定諤方程特征值問(wèn)題高效譜元方法、并行軟件與算法等方面取得了系列原創(chuàng)成果，在SISC, SNIUM, JCP等國(guó)際國(guó)內(nèi)高水平學(xué)術(shù)刊物上發(fā)表論文70余篇。

內(nèi)容介紹：In this talk, we present first some ideas and tools to explicitly construct $curl^2$-conforming spectral elements, which possess a hierarchical structure and can be categorized into the kernel space and non-kernel space of the curl operator. Then, we propose the $curl^2$-conforming spectral element approximation schemes together with their implementation algorithms to solve the quad-curl problems. Next, we study the $curl^2$-conforming spectral approximation. Notably, the polynomial degree in the kernel space affects the convergence rate in $L^2(\Omega)^2$-norm, but not those measured in $H(curl;\Omega)$- and $H(curl^2;\Omega)$-seminorms. This allows us to obtain eigenvalue approximations from the upper or lower side by choosing different polynomial degrees for the kernel space and non-kernel space of the curl operator. Finally, numerical results demonstrate the effectiveness and efficiency of our method.