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Operator Splitting and Local Time-Stepping Methods for Transport Problems in Fractured Porous Media
《Communications in Computational Physics》2023年第10期1215-1246,共32页Phuoc-Toan Huynh Yanzhao Cao Thi-Thao-Phuong Hoang 
partially supported by the US National Science Foundation under grant number DMS-1912626.
This paper is concerned with efficient numerical methods for the advectiondiffusion equation in a heterogeneous porous medium containing fractures.A dimensionally reduced fracture model is considered,in which the frac...
关键词：Domain decomposition reduced fracture model operator splitting nonconforming time grids time-dependent Steklov-Poincare operator optimized Schwarz waveform relaxation 
Bi-Orthogonal fPINN:A Physics-Informed Neural Network Method for Solving Time-Dependent Stochastic Fractional PDEs被引量：1
《Communications in Computational Physics》2023年第9期1133-1176,共44页Lei Ma Rongxin Li Fanhai Zeng Ling Guo George Em Karniadakis 
supported by the NSF of China(92270115,12071301)and the Shanghai Municipal Science and Technology Commission(20JC1412500);Fanhai Zeng is supported by the National Key R&D Program of China(2021YFA1000202,2021YFA1000200);the NSF of China(12171283,12120101001);the startup fund from Shandong University(11140082063130);the Science Foundation Program for Distinguished Young Scholars of Shandong(Overseas)(2022HWYQ-045).
Fractional partial differential equations(FPDEs)can effectively represent anomalous transport and nonlocal interactions.However,inherent uncertainties arise naturally in real applications due to random forcing or unkn...
关键词：Scientific machine learning uncertainty quantification stochastic fractional differential equations PINNs inverse problems 
Analysis and Application of Single Level, Multi-Level Monte Carlo and Quasi-Monte Carlo Finite Element Methods for Time-Dependent Maxwell’s Equations with Random Inputs
《Communications in Computational Physics》2021年第1期211-236,共26页Xiang Wang Jichun Li Zhiwei Fang 
supported by National Natural Science Foundation of China under grants No.11961048,No.11671340;NSF of Jiangxi Province with No.20181ACB20001.
This article is devoted to three quadrature methods for the rapid solution of stochastic time-dependent Maxwell’s equations with uncertain permittivity,perme-ability and initial conditions.We develop the mathematical...
关键词：Maxwell’s equations uncertainty quantification edge element 
A Novel Method for Solving Time-Dependent 2D Advection-Diffusion-Reaction Equations to Model Transfer in Nonlinear Anisotropic Media被引量：1
《Communications in Computational Physics》2019年第6期233-264,共32页Ji Lin Sergiy Reutskiy C.S.Chen Jun Lu 
supported by the Fundamental Research Funds for the Central Universities(No.2018B16714);the National Natural Science Foundation of China(Nos.11702083,11572111,51679150,51579153,51739008,51527811);the State Key Laboratory of Mechanics and Control of Mechanical Structures(Nanjing University of Aeronautics and Astronautics)(No.MCMS-0218G01);the China Postdoctoral Science Foundation(No.2017M611669);the China Postdoctoral Science Special Foundation(No.2018T110430);the Postdoctoral Foundation of Jiangsu Province(No.1701059C);the National Key R&D Program of China(No.2016YFC0401902);the Fund Project of NHRI(Nos.Y417002,Y417015).
This paper presents a new numerical technique for solving initial and bound-ary value problems with unsteady strongly nonlinear advection diffusion reaction(ADR)equations.The method is based on the use of the radial b...
关键词：Advection diffusion reaction TIME-DEPENDENT fully nonlinear anisotropic media Crank-Nicolson scheme meshless method 
Reduced Basis Approaches in Time-Dependent Non-Coercive Settings for Modelling the Movement of Nuclear Reactor Control Rods被引量：1
《Communications in Computational Physics》2016年第6期23-59,共37页Alberto Sartori Antonio Cammi Lelio Luzzi Gianluigi Rozza 
We acknowledge CINECA and Regione Lombardia LISA computational initiative,for the availability of high performance computing resources and support.G.Rozza acknowledges INDAM-GNCS national activity group and NOFYSAS program of SISSA.
In this work,two approaches,based on the certified Reduced Basis method,have been developed for simulating the movement of nuclear reactor control rods,in time-dependent non-coercive settings featuring a 3D geometrica...
关键词：Reduced basis method control rod movement spatial kinetics parametrized geometry multi-group neutron diffusion non-coercive operators 
Velocity-Based Moving Mesh Methods for Nonlinear Partial Differential Equations
《Communications in Computational Physics》2011年第8期509-576,共68页M.J.Baines M.E.Hubbard P.K.Jimack 
This article describes a number of velocity-based moving mesh numerical methods for multidimensional nonlinear time-dependent partial differential equations(PDEs).It consists of a short historical review followed by a...
关键词：Time-dependent nonlinear diffusion moving boundaries finite element method Lagrangian meshes conservation of mass 
Local Discontinuous Galerkin Methods for High-Order Time-Dependent Partial Differential Equations被引量：13
《Communications in Computational Physics》2010年第1期1-46,共46页Yan Xu Chi-Wang Shu 
The research of the first author is support by NSFC grant 10601055,FANEDD of CAS and SRF for ROCS SEM;The research of the second author is supported by NSF grant DMS-0809086 and DOE grant DE-FG02-08ER25863.
Discontinuous Galerkin (DG) methods are a class of finite element methodsusing discontinuous basis functions, which are usually chosen as piecewise polynomi-als. Since the basis functions can be discontinuous, these m...
关键词：Discontinuous Galerkin method local discontinuous Galerkin method numerical flux STABILITY time discretization high order accuracy STABILITY error estimates 
A Finite Element Method Solver for Time-Dependent and Stationary Schrodinger Equations with a Generic Potential
《Communications in Computational Physics》2009年第5期914-927,共14页A.Soba 
A general finite element solution of the Schrodinger equation for a onedimensional problem is presented.The solver is applicable to both stationary and time-dependent cases with a general user-selected potential term....
关键词：One dimensional finite element methods time dependent Schrodinger equation periodic boundary conditions quantum computer simulation 
Splitting Finite Difference Methods on Staggered Grids for the Three-Dimensional Time-Dependent Maxwell Equations被引量：1
《Communications in Computational Physics》2008年第7期405-432,共28页Liping Gao Bo Zhang Dong Liang 
In this paper,we study splitting numerical methods for the three-dimensional Maxwell equations in the time domain.We propose a new kind of splitting finitedifference time-domain schemes on a staggered grid,which consi...
关键词：Splitting scheme alternating direction implicit method finite-difference time-domain method stability CONVERGENCE Maxwell’s equations perfectly conducting boundary 
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