Mesh-free finite difference(FD)methods can improve the geometric flexibility of modeling without the need for lattice mapping or complex meshing process.Radial-basisfunction-generated FD is among the most commonly use...Mesh-free finite difference(FD)methods can improve the geometric flexibility of modeling without the need for lattice mapping or complex meshing process.Radial-basisfunction-generated FD is among the most commonly used mesh-free FD methods and can accurately simulate seismic wave propagation in the non-rectangular computational domain.In this paper,we propose a perfectly matched layer(PML)boundary condition for a meshfree FD solution of the elastic wave equation,which can be applied to the boundaries of the non-rectangular velocity model.The performance of the PML is,however,severely reduced for near-grazing incident waves and low-frequency waves.We thus also propose the complexfrequency-shifted PML(CFS-PML)boundary condition for a mesh-free FD solution of the elastic wave equation.For two PML boundary conditions,we derive unsplit time-domain expressions by constructing auxiliary differential equations,both of which require less memory and are easy for programming.Numerical experiments demonstrate that these two PML boundary conditions effectively eliminate artificial boundary reflections in mesh-free FD simulations.When compared with the PML boundary condition,the CFS-PML boundary condition results in better absorption for near-grazing incident waves and evanescent waves.展开更多
For the transient behavior of a semiconductor device, the modified method of characteristics with alternating-direction finite element procedures for nonrectangular region is put forward. Some techniques, such as calc...For the transient behavior of a semiconductor device, the modified method of characteristics with alternating-direction finite element procedures for nonrectangular region is put forward. Some techniques, such as calculus of variations, isoparametric transformation，patch approximation, operator-splitting, characteristic method, symmetrical reflection,energy method, negative norm estimate and a prior estimates and techniques, are employed. In the nonrectangular region case, optimal order estimates in L^2 norm are derived for the error in the approximation solution. Thus the well-known theoretical problem has been thoroughly and completely solved.展开更多
For coupled system of multilayer dynamics of fluids in porous media, thecharacteristic alternating-direction finite element methods for nonrectangular regions applicable toparallel arithmetic are put forward and two-d...For coupled system of multilayer dynamics of fluids in porous media, thecharacteristic alternating-direction finite element methods for nonrectangular regions applicable toparallel arithmetic are put forward and two-dimensional and three-dimensional schemes are used toform a complete set. Some techniques, such as calculus of variations, isoparametric transformation,patch approximation, operator-splitting, characteristic method, negative norm estimate, energymethod, the theory of prior estimates and techniques are used. For the nonrectangular regions case,optimal order estimates in L^2 norm are derived for the error in the approximation solution. Thusthe well-known theoretical problem has been thoroughly and completely solved. These methods havebeen successfully used in multilayer oil resources migration-accumulation numerical simulation.展开更多
基金supported by the National Science and Technology Major Project(2016ZX05006-002)the National Natural Science Foundation of China(Nos.41874153,41504097)
文摘Mesh-free finite difference(FD)methods can improve the geometric flexibility of modeling without the need for lattice mapping or complex meshing process.Radial-basisfunction-generated FD is among the most commonly used mesh-free FD methods and can accurately simulate seismic wave propagation in the non-rectangular computational domain.In this paper,we propose a perfectly matched layer(PML)boundary condition for a meshfree FD solution of the elastic wave equation,which can be applied to the boundaries of the non-rectangular velocity model.The performance of the PML is,however,severely reduced for near-grazing incident waves and low-frequency waves.We thus also propose the complexfrequency-shifted PML(CFS-PML)boundary condition for a mesh-free FD solution of the elastic wave equation.For two PML boundary conditions,we derive unsplit time-domain expressions by constructing auxiliary differential equations,both of which require less memory and are easy for programming.Numerical experiments demonstrate that these two PML boundary conditions effectively eliminate artificial boundary reflections in mesh-free FD simulations.When compared with the PML boundary condition,the CFS-PML boundary condition results in better absorption for near-grazing incident waves and evanescent waves.
基金This research is supported by the Major State Basic Research Program of China (Grant No. 19990328), the National Tackling Key Problem Program, the National Science Foundation of China (Grant Nos. 10271066 and 10372052), the Doctorate Foundation of th
文摘For the transient behavior of a semiconductor device, the modified method of characteristics with alternating-direction finite element procedures for nonrectangular region is put forward. Some techniques, such as calculus of variations, isoparametric transformation，patch approximation, operator-splitting, characteristic method, symmetrical reflection,energy method, negative norm estimate and a prior estimates and techniques, are employed. In the nonrectangular region case, optimal order estimates in L^2 norm are derived for the error in the approximation solution. Thus the well-known theoretical problem has been thoroughly and completely solved.
基金This research is supported by the Major State Basic Research of China, the National Foundation of China and the National Key-Problems-Tackling Program of China.
文摘For coupled system of multilayer dynamics of fluids in porous media, thecharacteristic alternating-direction finite element methods for nonrectangular regions applicable toparallel arithmetic are put forward and two-dimensional and three-dimensional schemes are used toform a complete set. Some techniques, such as calculus of variations, isoparametric transformation,patch approximation, operator-splitting, characteristic method, negative norm estimate, energymethod, the theory of prior estimates and techniques are used. For the nonrectangular regions case,optimal order estimates in L^2 norm are derived for the error in the approximation solution. Thusthe well-known theoretical problem has been thoroughly and completely solved. These methods havebeen successfully used in multilayer oil resources migration-accumulation numerical simulation.
