| 1. |
- Clayton, R, et al.
(författare)
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Absorbing boundary conditions for acoustic and elastic wave equations
- 1977
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Ingår i: Bulletin of The Seismological Society of America (BSSA). - : Elsevier BV. - 0037-1106 .- 1943-3573. ; 67:6, s. 1529-1540
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Tidskriftsartikel (refereegranskat)abstract
- The two dimensional elastic wave equations are used to model wave propagation in mediums with large or unbounded domains. In order to numerically simulate those problems the equations have to be put on the computer and artificial boundary conditions that allow minimal wave reflection must be introduced. These boundary conditions are well known in the literature as absorbing or radiating boundary conditions. They have been of interest to physicists and meteorologists for some time. In this paper three different methods for deriving radiating boundary conditions for the elastic wave equations are presented. One of these techniques gives exact absorbing boundary conditions for both P (longitudinal) and S (transverse) waves generated from a surface source. From this, approximate absorbing boundary conditions are derived. These conditions are easy to employ in finite difference codes.
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| 2. |
- Engquist, Björn, et al.
(författare)
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A system for automatic code generation for hyperbolic problems
- 1975
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Ingår i: Signum Newsletter. - New York, New York, USA : ACM Press. ; 10, s. 20-22
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Tidskriftsartikel (refereegranskat)abstract
- DCG is a program which generates FORTRAN code for difference approximations from a mathematical specification of a hyperbolic system. In our system the user presents his problem in a mathematical notation. DCG analyses the problem, chooses algorithms and generates a complete program for the numerical integration. The main parts of DCG are a program for symbolic analysis, “the analyser”, a library of FORTRAN-code and a program, “the synthesiser” that composes a complete FORTRAN program using code from the library.
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| 3. |
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| 4. |
- Engquist, Björn, et al.
(författare)
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Difference and finite element methods for hyperbolic differential equations
- 1979
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Ingår i: Computer Methods in Applied Mechanics and Engineering. - : Elsevier BV. - 0045-7825 .- 1879-2138. ; 17-18:3, s. 581-596
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Tidskriftsartikel (refereegranskat)abstract
- In recent years finite element methods have started to be applied to hyperbolic equations. Since modern finite element and finite difference methods for hyperbolic equations look very much alike, new results in the analysis of difference methods are also applicable to element methods. We shall discuss propagation of sharp signals, problems with different time scales and the effect of boundaries on stability and accuracy.
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| 5. |
- Engquist, Björn, et al.
(författare)
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Numerical solution of a PDE system describing a catalytic converter
- 1978
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Ingår i: Journal of Computational Physics. - : Elsevier BV. - 0021-9991 .- 1090-2716. ; 27:3, s. 295-314
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Tidskriftsartikel (refereegranskat)abstract
- Numerical approximations are studied for a large hyperbolic system coupled to a parabolic equation and a system of algebraic equations. The equations, which all are nonlinear, describe nonviscous compressible one-dimensional gas flow in a catalytic converter. Chemical reactions within the gas are included in the model. Well-posedness of the partial differential equations is analyzed together with stability of the numerical models. In particular an investigation is made of the effect of numerical dissipation and different boundary conditions. Numerical results are presented.
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| 6. |
- Engquist, Björn, et al.
(författare)
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Radiation boundary conditions for acoustic and elastic wave calculations
- 1979
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Ingår i: Communications on Pure and Applied Mathematics. - : Wiley. - 0010-3640 .- 1097-0312. ; 32:3, s. 314-358
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Tidskriftsartikel (refereegranskat)abstract
- A technique for developing radiating boundary conditions for artificial computational boundaries is described and applied to a class of problems typical in exploration seismology involving acoustic and elastic wave equations. First, one considers a constant coefficient scalar wave equation where the artificial boundary is one edge of a rectangular domain. By using continued fraction expansions, a systematic sequence of stable highly absorbing boundary conditions with successively better absorbing properties as the order of the boundary conditions increases is obtained. There follows a systematic derivation of a hierarchy of local radiating boundary conditions for the elastic wave equation. A theoretical procedure to guarantee stability at corners of the rectangular domain is worked out. A technique for fitting the discrete radiating boundary conditions directly to the difference scheme itself is proposed.
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