| 1. |
- Atle, Andreas, 1972-
(författare)
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Approximations of Integral Equations for WaveScattering
- 2006
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Wave scattering is the phenomenon in which a wave field interacts with physical objects. An incoming wave is scattered at the surface of the object and a scattered wave is produced. Common practical cases are acoustic, electromagnetic and elastic wave scattering. The numerical simulation of the scattering process is important, for example, in noise control, antenna design, prediction of radar cross sections and nondestructive testing.Important classes of numerical methods for accurate simulation of scattering are based on integral representations of the wave fields and theses representations require the knowledge of potentials on the surfaces of the scattering objects. The potential is typically computed by a numerical approximation of an integral equation that is defined on the surface. We first develop such numerical methods in time domain for the scalar wave equation. The efficiency of the techniques are improved by analytic quadrature and in some cases by local approximation of the potential.Most scattering simulations are done for harmonic or single frequency waves. In the electromagnetic case the corresponding integral equation method is called the method of moments. This numerical approximation is computationally very costly for high frequency waves. A simplification is suggested by physical optics, which directly gives an approximation of the potential without the solution of an integral equation. Physical optics is however only accurate for very high frequencies.In this thesis we improve the accuracy in the physical optics approximation of scalar waves by basing the computation of the potential on the theory of radiation boundary conditions. This theory describes the local coupling of derivatives in the wave field and if it is applied at the surface of the scattering object it generates an expression for the unknown potential. The full wave field is then computed as for other integral equation methods.The new numerical techniques are analyzed mathematically and their efficiency is established in a sequence of numerical experiments. The new on surface radiation conditions give, for example, substantial improvement in the estimation of the scattered waves in the acoustic case. This numerical experiment corresponds to radar cross-section estimation in the electromagnetic case.
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| 2. |
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| 3. |
- Engquist, Björn, et al.
(författare)
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Analysis of HMM for One Dimensional Wave Propagation Problems Over Long Time
- 2011
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Tidskriftsartikel (refereegranskat)abstract
- Multiscale problems are computationally costly to solve by direct simulation because the smallest scales must be represented over a domain determined by the largest scales of the problem. We have developed and analyzed new numerical methods for multiscale wave propagation following the framework of the heterogeneous multiscale method. The numerical methods couple simulations on macro- and microscales for problems with rapidly fluctuating material coefficients. The computational complexity of the new method is significantly lower than that of traditional techniques. We focus on HMM approximation applied to long time integration of one-dimensional wave propagation problems in both periodic and non-periodic medium and show that the dispersive effect that appear after long time is fully captured.
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| 4. |
- Engquist, Björn, et al.
(författare)
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Automatic analysis in PDE software
- 1984
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Ingår i: PDE Software. - Amsterdam, The Netherlands : Elsevier Science. - 0444876200 ; , s. 399-409
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Konferensbidrag (refereegranskat)
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| 5. |
- Engquist, Björn, et al.
(författare)
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Automatic computer code generation for hyperbolic and parabolic differential equations
- 1980
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Ingår i: SIAM JOURNAL ON SCIENTIFIC AND STATISTICAL COMPUTING. - : Society for Industrial & Applied Mathematics (SIAM). - 0196-5204 .- 2168-3417. ; 1:2, s. 249-259
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Tidskriftsartikel (refereegranskat)abstract
- A program system which generates computer code for the numerical solution of systems of hyperbolic and parabolic differential equations is described. The input to the program is a mathematical formulation of a hyperbolic or parabolic initial boundary value problem in one space dimension. The differential equations and boundary conditions are analyzed by the program system, and a finite difference algorithm is designed for the given problem. The output is an executable FORTRAN program.
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| 6. |
- 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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| 7. |
- Engquist, Björn, et al.
(författare)
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High Order shock capturing methods
- 1995
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Ingår i: Computational Fluid Dynamics Review. - New York : John Wiley & Sons. - 0471955892 ; , s. 210-233
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Bokkapitel (refereegranskat)
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| 8. |
- Engquist, Björn
(författare)
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Inverse imaging methods in exploration seismology
- 1980
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Ingår i: Computing Methods in Applied Sciences and Engineering. - Amsterdam, The Netherlands : Elsevier Science. ; , s. 547-552
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Konferensbidrag (refereegranskat)
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| 9. |
- Engquist, Björn, et al.
(författare)
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Multiscale Methods for One Dimensional Wave Propagation with High Frequency Initial Data
- 2011
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- High frequency wave propagation problems are computationally costly to solve by traditional techniques because the short wavelength must be well represented over a domain determined by the largest scales of the problem. We have developed and analyzed a new numerical method for high frequency wave propagation in the framework of heterogeneous multiscale methods, closely related to the analytical method of geometrical optics. The numerical method couples simulations on macro- and micro-scales for problems with highly oscillatory initial data. The method has a computational complexity essentially independent of the wavelength. We give one numerical example with a sharp but regular jump in velocity on the microscopic scale for which geometrical optics fails but our HMM gives correct results. We briefly discuss how the method can be extended to higher dimensional problems.
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| 10. |
- Engquist, Björn, et al.
(författare)
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Multiscale methods for the wave equation
- 2007
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Ingår i: PAMM · Proc. Appl. Math. Mech. 7. - : Wiley. ; , s. 1140903-1140904
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Konferensbidrag (övrigt vetenskapligt/konstnärligt)abstract
- We consider the wave equation in a medium with a rapidly varying speed of propagation. We construct a multiscale schemebased on the heterogeneous multiscale method, which can compute the correct coarse behavior of wave pulses traveling in themedium, at a computational cost essentially independent of the size of the small scale variations. This is verified by theoreticalresults and numerical examples.
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