主講人：仲杏慧 浙江大學(xué)教授

時(shí)間：2022年5月31日10：00

地點(diǎn)：騰訊會(huì)議 482 114 740

舉辦單位：數(shù)理學(xué)院

主講人介紹：仲杏慧，2007年獲中國(guó)科學(xué)技術(shù)大學(xué)學(xué)士學(xué)位，2012年獲美國(guó)布朗大學(xué)博士學(xué)位。隨后在密歇根州立大學(xué)和猶他大學(xué)從事博士后研究工作?，F(xiàn)任浙江大學(xué)百人計(jì)劃研究員、博士生導(dǎo)師。研究方向?yàn)閿?shù)值分析，科學(xué)計(jì)算，不確定性量化等領(lǐng)域，主要研究工作包括間斷有限元方法的算法設(shè)計(jì)及其分析、動(dòng)力學(xué)傳輸方程的數(shù)值模擬及其在等離子體物理中的應(yīng)用、不確定量化及隨機(jī)計(jì)算算法及應(yīng)用等方面。

內(nèi)容介紹：In this talk, we present finite difference weighted essentially non-oscillatory (WENO) schemes with unequal-sized sub-stencils for solving the Degasperis-Procesi (DP) and μ- Degasperis-Procesi (μDP) equations, which contain nonlinear high order derivatives, and possibly peakon solutions or shock waves. By introducing auxiliary variable(s), we rewrite the DP equation as a hyperbolic-elliptic system, and the μDP equation as a first order system. Then we choose a linear finite difference scheme with suitable order of accuracy for the auxiliary variable(s), and finite difference WENO schemes with unequal-sized sub-stencils for the primal variable. Comparing with the classical WENO scheme which uses several small stencils of the same size to make up a big stencil, WENO schemes with unequal-sized sub-stencils are simple in the choice of the stencil and enjoy the freedom of arbitrary positive linear weights. Another advantage is that the final reconstructed polynomial on the target cell is a polynomial of the same degree as the polynomial over the big stencil, while the classical finite difference WENO reconstruction can only be obtained for specific points inside the target interval. Numerical tests are provided to demonstrate the high order accuracy and non-oscillatory properties of the proposed schemes.