{"id":374,"date":"2026-09-22T01:01:47","date_gmt":"2026-09-22T01:01:47","guid":{"rendered":"https:\/\/chunchiliu.com\/?page_id=374"},"modified":"2026-09-24T03:51:18","modified_gmt":"2026-09-24T03:51:18","slug":"homepage-2","status":"publish","type":"page","link":"https:\/\/chunchiliu.com\/cn\/","title":{"rendered":"Homepage"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-page\" data-elementor-id=\"374\" class=\"elementor elementor-374\" data-elementor-post-type=\"page\">\n\t\t\t\t<div class=\"elementor-element elementor-element-d23120e e-flex e-con-boxed e-con e-parent\" data-id=\"d23120e\" data-element_type=\"container\" data-e-type=\"container\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t<div class=\"elementor-element elementor-element-becc631 e-con-full e-flex e-con e-child\" data-id=\"becc631\" data-element_type=\"container\" data-e-type=\"container\" data-settings=\"{&quot;motion_fx_motion_fx_scrolling&quot;:&quot;yes&quot;,&quot;motion_fx_devices&quot;:[&quot;desktop&quot;,&quot;tablet&quot;,&quot;mobile&quot;]}\">\n\t\t<div class=\"elementor-element elementor-element-ba1a1b8 e-con-full e-flex e-con e-child\" data-id=\"ba1a1b8\" data-element_type=\"container\" data-e-type=\"container\">\n\t\t\t\t<div class=\"elementor-element elementor-element-6118808 elementor-widget elementor-widget-image\" data-id=\"6118808\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<img fetchpriority=\"high\" decoding=\"async\" width=\"797\" height=\"1024\" src=\"https:\/\/chunchiliu.com\/wp-content\/uploads\/2026\/06\/chunchi-liu-797x1024.jpg\" class=\"attachment-large size-large wp-image-201\" alt=\"Image of Chunchi Liu\" srcset=\"https:\/\/chunchiliu.com\/wp-content\/uploads\/2026\/06\/chunchi-liu-797x1024.jpg 797w, https:\/\/chunchiliu.com\/wp-content\/uploads\/2026\/06\/chunchi-liu-233x300.jpg 233w, https:\/\/chunchiliu.com\/wp-content\/uploads\/2026\/06\/chunchi-liu-768x987.jpg 768w, https:\/\/chunchiliu.com\/wp-content\/uploads\/2026\/06\/chunchi-liu.jpg 827w\" sizes=\"(max-width: 797px) 100vw, 797px\" \/>\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-d59c497 e-con-full e-flex e-con e-child\" data-id=\"d59c497\" data-element_type=\"container\" data-e-type=\"container\">\n\t\t\t\t<div class=\"elementor-element elementor-element-cf2e23b elementor-invisible elementor-widget elementor-widget-heading\" data-id=\"cf2e23b\" data-element_type=\"widget\" data-e-type=\"widget\" data-settings=\"{&quot;_animation&quot;:&quot;fadeInUp&quot;}\" data-widget_type=\"heading.default\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">Postdoctoral Researcher at <br>\nShanghai Jiao Tong University<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-25121a1 elementor-invisible elementor-widget elementor-widget-heading\" data-id=\"25121a1\" data-element_type=\"widget\" data-e-type=\"widget\" data-settings=\"{&quot;_animation&quot;:&quot;fadeInUp&quot;}\" data-widget_type=\"heading.default\">\n\t\t\t\t\t<h1 class=\"elementor-heading-title elementor-size-default\">Chunchi Liu<\/h1>\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-e0105c3 animated-slow elementor-invisible elementor-widget elementor-widget-image\" data-id=\"e0105c3\" data-element_type=\"widget\" data-e-type=\"widget\" data-settings=\"{&quot;_animation&quot;:&quot;fadeIn&quot;}\" data-widget_type=\"image.default\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<img decoding=\"async\" width=\"357\" height=\"22\" src=\"https:\/\/chunchiliu.com\/wp-content\/uploads\/2026\/09\/Clip-path-group.png\" class=\"attachment-large size-large wp-image-449\" alt=\"\" srcset=\"https:\/\/chunchiliu.com\/wp-content\/uploads\/2026\/09\/Clip-path-group.png 357w, https:\/\/chunchiliu.com\/wp-content\/uploads\/2026\/09\/Clip-path-group-300x18.png 300w, https:\/\/chunchiliu.com\/wp-content\/uploads\/2026\/09\/Clip-path-group-18x1.png 18w\" sizes=\"(max-width: 357px) 100vw, 357px\" \/>\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-ee6c0ee elementor-widget elementor-widget-text-editor\" data-id=\"ee6c0ee\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t\t\t\t\t\t<p>Dr. Chunchi Liu is a postdoctoral researcher at the Institute of Natural Sciences, Shanghai Jiao Tong University. She received her Ph.D. from East China Normal University in 2025.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-d1782d7 e-con-full e-flex e-con e-child\" data-id=\"d1782d7\" data-element_type=\"container\" data-e-type=\"container\">\n\t\t\t\t<div class=\"elementor-element elementor-element-8c31c77 elementor-widget elementor-widget-button\" data-id=\"8c31c77\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t\t\t\t\t\t\t<a class=\"elementor-button elementor-button-link elementor-size-sm\" href=\"#\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t\t\t\t<span class=\"elementor-button-text\">About Me<\/span>\n\t\t\t\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-b949f6a elementor-widget elementor-widget-button\" data-id=\"b949f6a\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t\t\t\t\t\t\t<a class=\"elementor-button elementor-button-link elementor-size-sm\" href=\"https:\/\/chunchiliu.com\/cn\/research\/\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t\t\t\t<span class=\"elementor-button-text\">Publications<\/span>\n\t\t\t\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-cc37095 e-flex e-con-boxed e-con e-parent\" data-id=\"cc37095\" data-element_type=\"container\" data-e-type=\"container\" data-settings=\"{&quot;background_background&quot;:&quot;classic&quot;,&quot;motion_fx_motion_fx_scrolling&quot;:&quot;yes&quot;,&quot;motion_fx_devices&quot;:[&quot;desktop&quot;,&quot;tablet&quot;,&quot;mobile&quot;]}\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-2c8bb3e e-flex e-con-boxed e-con e-parent\" data-id=\"2c8bb3e\" data-element_type=\"container\" data-e-type=\"container\" data-settings=\"{&quot;background_background&quot;:&quot;classic&quot;,&quot;motion_fx_motion_fx_scrolling&quot;:&quot;yes&quot;,&quot;motion_fx_translateY_effect&quot;:&quot;yes&quot;,&quot;motion_fx_translateY_speed&quot;:{&quot;unit&quot;:&quot;px&quot;,&quot;size&quot;:4,&quot;sizes&quot;:[]},&quot;motion_fx_translateY_affectedRange&quot;:{&quot;unit&quot;:&quot;%&quot;,&quot;size&quot;:&quot;&quot;,&quot;sizes&quot;:{&quot;start&quot;:0,&quot;end&quot;:100}},&quot;motion_fx_devices&quot;:[&quot;desktop&quot;,&quot;tablet&quot;,&quot;mobile&quot;]}\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t<div class=\"elementor-element elementor-element-7631b68 e-con-full e-flex e-con e-child\" data-id=\"7631b68\" data-element_type=\"container\" data-e-type=\"container\">\n\t\t<div class=\"elementor-element elementor-element-2fe4ec5 e-con-full e-flex e-con e-child\" data-id=\"2fe4ec5\" data-element_type=\"container\" data-e-type=\"container\">\n\t\t\t\t<div class=\"elementor-element elementor-element-a2ea3be elementor-widget elementor-widget-heading\" data-id=\"a2ea3be\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">RESEARCH FOCUS<\/h2>\t\t\t\t<\/div>\n\t\t\t\t\t\n<hr class=\"e-068414b-0b8c628 e-divider-base\" data-interaction-id=\"068414b\"   \/>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-8af4ae7 e-con-full e-flex e-con e-child\" data-id=\"8af4ae7\" data-element_type=\"container\" data-e-type=\"container\">\n\t\t\t\t<div class=\"elementor-element elementor-element-31a5473 elementor-widget elementor-widget-text-editor\" data-id=\"31a5473\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t\t\t\t\t\t<p>Her research lies in numerical analysis and scientific computing, with particular interests in numerical methods for partial differential equations, stochastic and parametric problems and dynamical low-rank approximation. Her current research focuses on randomized low-rank methods for structure-preserving simulations of open quantum systems, especially the Lindblad master equation.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-3da63c8 e-con-full e-flex e-con e-child\" data-id=\"3da63c8\" data-element_type=\"container\" data-e-type=\"container\">\n\t\t<div class=\"elementor-element elementor-element-94a697d e-con-full e-flex e-con e-child\" data-id=\"94a697d\" data-element_type=\"container\" data-e-type=\"container\" data-settings=\"{&quot;background_background&quot;:&quot;classic&quot;}\">\n\t\t<div class=\"elementor-element elementor-element-a489494 e-con-full e-flex e-con e-child\" data-id=\"a489494\" data-element_type=\"container\" data-e-type=\"container\" data-settings=\"{&quot;background_background&quot;:&quot;classic&quot;}\">\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-e677d87 elementor-widget elementor-widget-heading\" data-id=\"e677d87\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">Stokes-Darcy Systems<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-df8b6ef elementor-widget elementor-widget-text-editor\" data-id=\"df8b6ef\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t\t\t\t\t\t<p>Stable and efficient finite element methods for coupled free flow and porous media models<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-11970aa e-con-full e-flex e-con e-child\" data-id=\"11970aa\" data-element_type=\"container\" data-e-type=\"container\" data-settings=\"{&quot;background_background&quot;:&quot;classic&quot;}\">\n\t\t<div class=\"elementor-element elementor-element-11ebb65 e-con-full e-flex e-con e-child\" data-id=\"11ebb65\" data-element_type=\"container\" data-e-type=\"container\" data-settings=\"{&quot;background_background&quot;:&quot;classic&quot;}\">\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-d1c6581 elementor-widget elementor-widget-heading\" data-id=\"d1c6581\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">Random PDEs and UQ<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-f459cfa elementor-widget elementor-widget-text-editor\" data-id=\"f459cfa\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t\t\t\t\t\t<p>Monte Carlo, stochastic collocation, and uncertainty quantification methods for random Stokes-Darcy problems with uncertain parameters.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-264fa27 e-con-full e-flex e-con e-child\" data-id=\"264fa27\" data-element_type=\"container\" data-e-type=\"container\" data-settings=\"{&quot;background_background&quot;:&quot;classic&quot;}\">\n\t\t<div class=\"elementor-element elementor-element-8582914 e-con-full e-flex e-con e-child\" data-id=\"8582914\" data-element_type=\"container\" data-e-type=\"container\" data-settings=\"{&quot;background_background&quot;:&quot;classic&quot;}\">\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-183b89e elementor-widget elementor-widget-heading\" data-id=\"183b89e\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">Ensemble Domain Decomposition<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-ac3bf01 elementor-widget elementor-widget-text-editor\" data-id=\"ac3bf01\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t\t\t\t\t\t<p>Efficient ensemble and domain decomposition algorithms for repeated large-scale simulations, reducing computational cost across multiple realizations.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-b8b7f14 e-con-full e-flex e-con e-child\" data-id=\"b8b7f14\" data-element_type=\"container\" data-e-type=\"container\" data-settings=\"{&quot;background_background&quot;:&quot;classic&quot;}\">\n\t\t<div class=\"elementor-element elementor-element-9c31661 e-con-full e-flex e-con e-child\" data-id=\"9c31661\" data-element_type=\"container\" data-e-type=\"container\" data-settings=\"{&quot;background_background&quot;:&quot;classic&quot;}\">\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-46a0d11 elementor-widget elementor-widget-heading\" data-id=\"46a0d11\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">Open Quantum Systems<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-19deca0 elementor-widget elementor-widget-text-editor\" data-id=\"19deca0\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t\t\t\t\t\t<p>Randomized low-rank approximation methods for Lindblad dynamics, with emphasis on positive semidefinite structure and efficient simulation.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-6153654 e-flex e-con-boxed e-con e-parent\" data-id=\"6153654\" data-element_type=\"container\" data-e-type=\"container\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t<div class=\"elementor-element elementor-element-346892b e-con-full e-flex e-con e-child\" data-id=\"346892b\" data-element_type=\"container\" data-e-type=\"container\">\n\t\t<div class=\"elementor-element elementor-element-f1e44a8 e-con-full e-flex e-con e-child\" data-id=\"f1e44a8\" data-element_type=\"container\" data-e-type=\"container\">\n\t\t\t\t<div class=\"elementor-element elementor-element-1c6a4cd elementor-widget elementor-widget-heading\" data-id=\"1c6a4cd\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">RECENT PUBLICATIONS<\/h2>\t\t\t\t<\/div>\n\t\t\t\t\t\n<hr class=\"e-eadcd77-3351ecb e-divider-base\" data-interaction-id=\"eadcd77\"   \/>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-7a0cb03 e-con-full elementor-hidden-tablet elementor-hidden-mobile e-flex e-con e-child\" data-id=\"7a0cb03\" data-element_type=\"container\" data-e-type=\"container\">\n\t\t\t\t<div class=\"elementor-element elementor-element-cd4c909 e-transform elementor-widget elementor-widget-button\" data-id=\"cd4c909\" data-element_type=\"widget\" data-e-type=\"widget\" data-settings=\"{&quot;_transform_translateX_effect_hover&quot;:{&quot;unit&quot;:&quot;px&quot;,&quot;size&quot;:-12,&quot;sizes&quot;:[]},&quot;_transform_translateX_effect_hover_tablet&quot;:{&quot;unit&quot;:&quot;px&quot;,&quot;size&quot;:&quot;&quot;,&quot;sizes&quot;:[]},&quot;_transform_translateX_effect_hover_mobile&quot;:{&quot;unit&quot;:&quot;px&quot;,&quot;size&quot;:&quot;&quot;,&quot;sizes&quot;:[]},&quot;_transform_translateY_effect_hover&quot;:{&quot;unit&quot;:&quot;px&quot;,&quot;size&quot;:&quot;&quot;,&quot;sizes&quot;:[]},&quot;_transform_translateY_effect_hover_tablet&quot;:{&quot;unit&quot;:&quot;px&quot;,&quot;size&quot;:&quot;&quot;,&quot;sizes&quot;:[]},&quot;_transform_translateY_effect_hover_mobile&quot;:{&quot;unit&quot;:&quot;px&quot;,&quot;size&quot;:&quot;&quot;,&quot;sizes&quot;:[]}}\" data-widget_type=\"button.default\">\n\t\t\t\t\t\t\t\t\t\t<a class=\"elementor-button elementor-button-link elementor-size-sm\" href=\"https:\/\/chunchiliu.com\/cn\/research\/\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t\t\t\t<span class=\"elementor-button-text\">View All &gt;<\/span>\n\t\t\t\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-1ec9be0 e-con-full e-flex e-con e-child\" data-id=\"1ec9be0\" data-element_type=\"container\" data-e-type=\"container\">\n\t\t\t\t<div class=\"elementor-element elementor-element-4bed972 elementor-widget__width-initial elementor-widget elementor-widget-heading\" data-id=\"4bed972\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">2026<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-1676499 elementor-widget__width-initial elementor-widget-tablet__width-initial elementor-widget elementor-widget-text-editor\" data-id=\"1676499\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t\t\t\t\t\t<p style=\"margin-bottom: 10px;\">Multi-level Monte Carlo ensemble domain decomposition method for the random Stokes-Darcy models with uncertain parameters<\/p><p style=\"margin-bottom: 10px;\">Chunchi Liu, Yao Rong*, Yizhong Sun*, Jiaping Yu, Haibiao Zheng<\/p><p style=\"color: #868686; margin-bottom: 10px;\">Journal of Computational Physics, 556, Article 114800, 2026.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-1fc7142 elementor-widget elementor-widget-button\" data-id=\"1fc7142\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t\t\t\t\t\t\t<a class=\"elementor-button elementor-button-link elementor-size-sm\" href=\"https:\/\/www.sciencedirect.com\/science\/article\/pii\/S0021999126001506\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t\t\t\t<span class=\"elementor-button-text\">DOI<\/span>\n\t\t\t\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-3175266 e-con-full e-flex e-con e-child\" data-id=\"3175266\" data-element_type=\"container\" data-e-type=\"container\">\n\t\t\t\t<div class=\"elementor-element elementor-element-fb85bb2 elementor-widget elementor-widget-spacer\" data-id=\"fb85bb2\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"spacer.default\">\n\t\t\t\t\t\t\t<div class=\"elementor-spacer\">\n\t\t\t<div class=\"elementor-spacer-inner\"><\/div>\n\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-b597546 elementor-widget__width-initial elementor-widget-tablet__width-initial elementor-widget elementor-widget-text-editor\" data-id=\"b597546\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t\t\t\t\t\t<p style=\"margin-bottom: 10px;\">An ensemble domain decomposition method based on the stochastic collocation method for the random Stokes-Darcy models<\/p><p style=\"margin-bottom: 10px;\">Yan Chen, <strong>Chunchi Liu*<\/strong>, and Haibiao Zheng<\/p><p style=\"color: #868686; margin-bottom: 10px;\">Computer Methods in Applied Mechanics and Engineering, 2026.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-834bac6 elementor-widget elementor-widget-button\" data-id=\"834bac6\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t\t\t\t\t\t\t<a class=\"elementor-button elementor-button-link elementor-size-sm\" href=\"https:\/\/www.sciencedirect.com\/science\/article\/abs\/pii\/S0045782526004482\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t\t\t\t<span class=\"elementor-button-text\">DOI<\/span>\n\t\t\t\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-6270492 e-con-full e-flex e-con e-child\" data-id=\"6270492\" data-element_type=\"container\" data-e-type=\"container\">\n\t\t\t\t<div class=\"elementor-element elementor-element-2019502 elementor-widget elementor-widget-spacer\" data-id=\"2019502\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"spacer.default\">\n\t\t\t\t\t\t\t<div class=\"elementor-spacer\">\n\t\t\t<div class=\"elementor-spacer-inner\"><\/div>\n\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-03b112a elementor-widget__width-initial elementor-widget-tablet__width-initial elementor-widget elementor-widget-text-editor\" data-id=\"03b112a\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t\t\t\t\t\t<p style=\"margin-bottom: 10px;\">A Long-Time Stable Higher-Order Time Discretization Scheme for Stochastic Stokes-Darcy Systems<\/p><p style=\"margin-bottom: 10px;\">Yan Chen, <strong>Chunchi Liu*<\/strong>, and Haibiao Zheng<\/p><p style=\"color: #868686; margin-bottom: 10px;\">(Under Review)<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-acf9a74 elementor-widget elementor-widget-spacer\" data-id=\"acf9a74\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"spacer.default\">\n\t\t\t\t\t\t\t<div class=\"elementor-spacer\">\n\t\t\t<div class=\"elementor-spacer-inner\"><\/div>\n\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-1878859 e-con-full elementor-hidden-desktop e-flex e-con e-child\" data-id=\"1878859\" data-element_type=\"container\" data-e-type=\"container\">\n\t\t\t\t<div class=\"elementor-element elementor-element-ed0ff7f e-transform elementor-widget elementor-widget-button\" data-id=\"ed0ff7f\" data-element_type=\"widget\" data-e-type=\"widget\" data-settings=\"{&quot;_transform_translateX_effect_hover&quot;:{&quot;unit&quot;:&quot;px&quot;,&quot;size&quot;:-12,&quot;sizes&quot;:[]},&quot;_transform_translateX_effect_hover_tablet&quot;:{&quot;unit&quot;:&quot;px&quot;,&quot;size&quot;:&quot;&quot;,&quot;sizes&quot;:[]},&quot;_transform_translateX_effect_hover_mobile&quot;:{&quot;unit&quot;:&quot;px&quot;,&quot;size&quot;:&quot;&quot;,&quot;sizes&quot;:[]},&quot;_transform_translateY_effect_hover&quot;:{&quot;unit&quot;:&quot;px&quot;,&quot;size&quot;:&quot;&quot;,&quot;sizes&quot;:[]},&quot;_transform_translateY_effect_hover_tablet&quot;:{&quot;unit&quot;:&quot;px&quot;,&quot;size&quot;:&quot;&quot;,&quot;sizes&quot;:[]},&quot;_transform_translateY_effect_hover_mobile&quot;:{&quot;unit&quot;:&quot;px&quot;,&quot;size&quot;:&quot;&quot;,&quot;sizes&quot;:[]}}\" data-widget_type=\"button.default\">\n\t\t\t\t\t\t\t\t\t\t<a class=\"elementor-button elementor-button-link elementor-size-sm\" href=\"https:\/\/chunchiliu.com\/cn\/research\/\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t\t\t\t<span class=\"elementor-button-text\">View All &gt;<\/span>\n\t\t\t\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t","protected":false},"excerpt":{"rendered":"<p>Postdoctoral Researcher at Shanghai Jiao Tong University Chunchi Liu Dr. Chunchi Liu is a postdoctoral researcher at the Institute of Natural Sciences, Shanghai Jiao Tong University. She received her Ph.D. from East China Normal University in 2025. About Me Publications RESEARCH FOCUS Her research lies in numerical analysis and scientific computing, with particular interests in [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"elementor_header_footer","meta":{"footnotes":""},"folder":[],"class_list":["post-374","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/chunchiliu.com\/cn\/wp-json\/wp\/v2\/pages\/374","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/chunchiliu.com\/cn\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/chunchiliu.com\/cn\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/chunchiliu.com\/cn\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/chunchiliu.com\/cn\/wp-json\/wp\/v2\/comments?post=374"}],"version-history":[{"count":102,"href":"https:\/\/chunchiliu.com\/cn\/wp-json\/wp\/v2\/pages\/374\/revisions"}],"predecessor-version":[{"id":505,"href":"https:\/\/chunchiliu.com\/cn\/wp-json\/wp\/v2\/pages\/374\/revisions\/505"}],"wp:attachment":[{"href":"https:\/\/chunchiliu.com\/cn\/wp-json\/wp\/v2\/media?parent=374"}],"wp:term":[{"taxonomy":"folder","embeddable":true,"href":"https:\/\/chunchiliu.com\/cn\/wp-json\/wp\/v2\/folder?post=374"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}