In this paper, we consider the acoustic impedance inversion problem of one dimensional wave equations. from the difference scheme of one diemsional wave equations, we derive the positive property of impulsive response...
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In this paper, we consider the acoustic impedance inversion problem of one dimensional wave equations. from the difference scheme of one diemsional wave equations, we derive the positive property of impulsive response in frequency domain,and prove that the positivity is a sufficient condition for the stability of impedance inversion.
The incompressible Navier-Stokes (INS) equations upon discretization on fixed meshes become a system of differential algebraic equations (DAE) of index 2. It is proved in this paper that for the general explicit and i...
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The incompressible Navier-Stokes (INS) equations upon discretization on fixed meshes become a system of differential algebraic equations (DAE) of index 2. It is proved in this paper that for the general explicit and implicit Runge-Kutta (RK)methods, the time accuracy of velocity is the same as that for the ordinary differential equations, by taking into consideration of the special form of the resulting DAE; (the time accuracy of pressure can be lower). For the three-stage secondorder explicit RK method, algorithms with less (than three) Poisson solutions of pressure are proposed and verified by numerical experiments. However, in practical computation of complex flows it is found that the method must satisfy the so-called consistency condition for the components of the solution (here the velocity and the pressure) of the DAE for the method to be robust.
We propose an approach to construct a C1 function on a fat surface domain, asurface that has thickness, by piecewise rational functions defined on a collection ofirregular triangular prisms. We show that the interpola...
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We propose an approach to construct a C1 function on a fat surface domain, asurface that has thickness, by piecewise rational functions defined on a collection ofirregular triangular prisms. We show that the interpolation function has algebraic precision 2. Examples that show the effectiveness of the scheme is presented.
In this paper parallel implementation issues concerning computation of a set ofrecurrences on distributed memory parallel systems are discussed. It is a commonproblem when solving partial differential equations on dis...
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In this paper parallel implementation issues concerning computation of a set ofrecurrences on distributed memory parallel systems are discussed. It is a commonproblem when solving partial differential equations on distributed memory systems,especially in computational fluid dynamics. For example, solution of a set of tri-diagonalsystems of equations or Guauss-Seidel relaxations on finite difference systems all leadto this kind of computation. We emphasize on the idea of doing the computations in apipelined fashion and we show through analysis and numerical examples that by usingproperly chosen parameters, pipelined implementation often yields much better parallelefficiency with respect to other commonly used methods.
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