A5101930655- Advanced Numerical Methods in Computational Mathematics
- Lattice Boltzmann Simulation Studies
- Numerical methods in engineering
- Advanced Mathematical Modeling in Engineering
- Computational Fluid Dynamics and Aerodynamics
- Electromagnetic Simulation and Numerical Methods
- Differential Equations and Numerical Methods
- Numerical methods for differential equations
- Topological Materials and Phenomena
- Fluid Dynamics and Turbulent Flows
- Fluid Dynamics and Thin Films
- Fluid Dynamics and Heat Transfer
- Drilling and Well Engineering
- Aerosol Filtration and Electrostatic Precipitation
- Enzyme Catalysis and Immobilization
- Quantum and electron transport phenomena
- Electromagnetic Scattering and Analysis
- Genomics and Phylogenetic Studies
- Microbial Metabolic Engineering and Bioproduction
- Hydraulic Fracturing and Reservoir Analysis
- Rheology and Fluid Dynamics Studies
- Rock Mechanics and Modeling
- Fluid Dynamics and Vibration Analysis
- Plant Gene Expression Analysis
- Differential Equations and Boundary Problems
Guizhou University
2022-2025
Guangxi University
2025
Sichuan University
2025
The Central Hospital of Xiao gan
2025
Wuhan University of Science and Technology
2025
Yunnan Agricultural University
2013-2025
Changchun University of Science and Technology
2025
Huizhou Central People's Hospital
2025
North Carolina State University
2015-2024
Xi'an Jiaotong University
2015-2024
The authors develop finite difference methods for elliptic equations of the form \[ \nabla \cdot (\beta (x)\nabla u(x)) + \kappa (x)u(x) = f(x)\] in a region $\Omega $ one or two space dimensions. It is assumed that simple (e.g., rectangle) and uniform rectangular grid used. situation studied which there an irregular surface $\Gamma codimension 1 contained across $\beta ,\kappa $, f may be discontinuous, along source have delta function singularity. As result, derivatives solution u...
A second-order accurate interface tracking method for the solution of incompressible Stokes flow problems with moving interfaces on a uniform Cartesian grid is presented. The may consist an elastic boundary immersed in fluid or between two different fluids. represented by cubic spline along which singularly supported surface tension force can be computed. equations are then discretized using finite difference methods elliptic singular sources developed our previous paper [SIAM J. Numer....
A fast, second-order accurate iterative method is proposed for the elliptic equation \[ \grad\cdot(\beta(x,y) \grad u) =f(x,y) \] in a rectangularregion $\Omega$ two-space dimensions. We assume that there an irregular interface across which coefficient $\beta$, solution u and its derivatives, and/or source term f may have jumps. are especially interested cases where coefficients $\beta$ piecewise constant jump large. The or not align with underlying Cartesian grid. idea our approach to...
In this work, a class of new finite-element methods, called immersed-interface is developed to solve elliptic interface problems with nonhomogeneous jump conditions. Simple non–body-fitted meshes are used. A single function that satisfies the same conditions constructed using level-set representation interface. With such function, discontinuities across in solution and flux removed, an equivalent problem homogeneous formulated. Special basis functions for nodal points near satisfy Error...
A model problem in electrical impedance tomography for the identification of unknown shapes from data a narrow strip along boundary domain is investigated. The representation shape and its evolution during an iterative reconstruction process achieved by level set method. derivatives this involve normal derivative potential boundary. Hence accurate resolution interface essential. It obtained immersed
Abstract This article discusses an immersed finite element (IFE) space introduced for solving a second‐order elliptic boundary value problem with discontinuous coefficients (interface problem). The IFE is nonconforming and its partition can be independent of the interface. error estimates interpolation function in usual Sobolev indicate that this has approximation capability similar to standard conforming linear based on body‐fit partitions. Numerical examples related method are provided. ©...
New finite difference methods using Cartesian grids are developed for elliptic interface problems with variable discontinuous coefficients, singular sources, and nonsmooth or even solutions. The new schemes constructed to satisfy the sign property of discrete maximum principle quadratic optimization techniques. shown converge under certain conditions comparison functions. coefficient matrix resulting linear system equations is an M-matrix coupled a multigrid solver. Numerical examples also...
The basis of the decline in circadian rhythms with aging was addressed by comparing patterns three behavioral young and old rats vitro rhythm neuronal activity suprachiasmatic nuclei (SCN), primary pacemaker. In some rats, body temperature, drinking, retained significant 24-h periodicities entraining light-dark cycles; others, one or two became aperiodic. When these were 23-27.5 mo they killed, single-unit firing rates SCN brain slices recorded continuously for 30 h. There damping mean peak...
Interface problems have many applications. Mathematically, interface usually lead to differential equations whose input data and solutions are non-smooth or discontinuous across some interfaces. The immersed method (IIM) has been developed in recent years particularly designed for problems. IIM is a sharp based on Cartesian grids. makes use of the jump conditions so that finite difference/element discretization can be accurate. In this survey paper, we will introduce various problems,...
New multigrid methods are developed for the maximum principle preserving immersed interface method applied to second order linear elliptic and parabolic PDEs that involve interfaces discontinuities. For problems, solver in this paper works while some other solvers do not. equations, we have finite difference scheme paper. We use Crank--Nicolson deal with diffusion part an explicit first derivatives. Numerical examples also presented.