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西安交通大学蒋耀林传授学术报告告诉

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biaotiwenti:waveform relaxation for partial differential equations

baogaoren:jiangyaolinchuanshou(xianjiaotongdaxueshuxueyutongjixueyuan)

baogaoshihou:2020nian9yue29ri 16:00-17:10

baogaodidian:qujiangxiaoqulixueyuanbaogaoting(jiaojiulou617)

zeyao: in this talk, we apply waveform relaxation (wr) to pdes directly at pdes level. compared with traditionally implementing wr to a large scale system of odes obtained by discretizing the spatial variables of the pdes, the information transmission between sub-systems can be avoided and the convergence rate does not deteriorate when the mesh is refined. picard wr at pdes level is first presented to show the advantages of the new approach. the estimation on iteration errors and two parallelisms of the wr are analyzed. next the approach is improved by quasi-newton relaxation and a theoretical framework of energy estimation for the superlinear convergence of some semi-linear pdes is developed. we then discuss the general wr at pdes level to obtain general convergence estimates for the single and coupled pdes. finally in several numerical experiments, we demonstrate the comparisons of iteration errors by four wr methods. the results suggest that the really new methods achieve excellent results after very few iterations and can be highly implemented in parallel.

baogaorenjianjie:

jiangyaolin,xianjiaotongdaxueerjichuanshou、bodao,jiaodaobuzhangjiangxuezhetepinchuanshou,jiaodaobukuashijiyouyirencai,guowuyuantebiebuzhuzhuanjia,xianjiaotongdaxueqifeitepinchuanshou,xianjiaotongdaxueshoupilingjunxuezhe。guodumixinshouyijiangpingshenren,jiaodaobutianranmixinjiangpingshenren,jiaodaoburencaijiajiangdasuanpingshenren,guoduliuxue(gongpai)jijindasuan、guowuyuanxueweiweiyuanhuizhongdianxuekehexueweidiandengpingshenren。shanxishengchanyeyuliyongshuxuexuehuilishizhang,zhongguochanyeyuliyongshuxuexuehuichangwulishi;shouyaochuzhiliyongshuxue、jijiaoshuxuefanchouneixiangganyantao。chushuxueshuzhushu4bu,banfaxueshuqikanlunwen300yupian,cizhongscijiansuoqikanlunwen260yupian(baohangefanchouguojizuiwenmingkanwurusiamxilieheieee transxiliedenglunwen);zhangguanguodujimingmu11xiang:3xiangkejibu863、973dengmingmuhe8xiangguodutianranmixinjijin;yantaogongxiaohuojiaodaobutianranmixinerdengjiang。

xiaowozhuye:


lixueyuan

2020nian9yue21ri



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