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Bayliss-Turkel-like radiation conditions on surfaces of arbitrary shape. (English) Zbl 0923.35179

The authors apply the pseudo-differential calculus to extend the Bayliss-Turkel second-order radiation condition to an arbitrary shaped surface. To this end, they use the Nirenberg factorization theorem which allows to calculate recursively symbols of pseudo-differential operators entering into an asymptotic expansion for the basic boundary pseudo-differential operator. As a by-product, known radiation conditions of order less that or equal to 2 are recovered, and their accuracy is discussed.
Reviewer: O.Titow (Berlin)

MSC:

35Q60 PDEs in connection with optics and electromagnetic theory
35S05 Pseudodifferential operators as generalizations of partial differential operators
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
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[1] X. Antoine, Conditions de radiation sur le bord, UFR Sciences, Université de Pau et des Pays de l’Adour, Pau, France, 1997; X. Antoine, Conditions de radiation sur le bord, UFR Sciences, Université de Pau et des Pays de l’Adour, Pau, France, 1997
[2] X. Antoine, Fast Computation of time-harmonic scattered field using the on-surface radiation condition method, J. Comput. Phys.; X. Antoine, Fast Computation of time-harmonic scattered field using the on-surface radiation condition method, J. Comput. Phys. · Zbl 1001.78008
[3] X. Antoine, H. Barucq, A. Bendali, Formulations symétriques dans le calcul de diffraction d’ondes par des conditions de radiation sur le bord, Univerisité de Pau et des Pays de l’Adour, France; X. Antoine, H. Barucq, A. Bendali, Formulations symétriques dans le calcul de diffraction d’ondes par des conditions de radiation sur le bord, Univerisité de Pau et des Pays de l’Adour, France
[4] X. Antoine, H. Barucq, A. Bendali, New absorbing boundary conditions including derivatives of the curvature for the two-dimensional Helmholtz equation, Université de Pau et des Pays de l’Adour, France; X. Antoine, H. Barucq, A. Bendali, New absorbing boundary conditions including derivatives of the curvature for the two-dimensional Helmholtz equation, Université de Pau et des Pays de l’Adour, France
[5] Bayliss, A.; Gunzburger, M.; Turkel, E., Boundary conditions for the numerical solution of elliptic equations in exterior regions, SIAM J. Appl. Math., 42, 430-451 (1982) · Zbl 0479.65056
[6] Chazarain, J.; Piriou, A., Introduction to the Theory of Linear Partial Differential Equations (1982), North-Holland: North-Holland Amsterdam/New York · Zbl 0487.35002
[7] Chen, G.; Zhou, J., Boundary Element Methods (1992), Academic Press, Harcourt Brace Jovanovitch: Academic Press, Harcourt Brace Jovanovitch San Diego
[8] Do Carmo, M. P., Differential Geometry of Curves and Surfaces (1976), Prentice Hall International: Prentice Hall International Englewood Cliffs · Zbl 0326.53001
[9] Engquist, B.; Majda, A., Absorbing boundary conditions for the numerical simulation of waves, Math. Comp., 31, 629-651 (1977) · Zbl 0367.65051
[10] L. Halpern, L. N. Trefethen, Wide-angle one-way wave equation, 86-5, Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA, July 1986; L. Halpern, L. N. Trefethen, Wide-angle one-way wave equation, 86-5, Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA, July 1986
[11] Hanouzet, B.; Sesquès, M., Absorbing boundary conditions for Maxwell’s equations, (Donato, A.; Olivieri, F., Non-Linear Hyperbolic Problems: Theoretical, Applied and Computational Aspects. Non-Linear Hyperbolic Problems: Theoretical, Applied and Computational Aspects, Notes Numer. Fluid Dynamics, 43 (1992)), 315-322 · Zbl 0922.65085
[12] Jin, J., The Finite Element Method in Electromagnetics (1993), Wiley: Wiley New York · Zbl 0823.65124
[13] Jones, D. S., Surface radiation conditions, IMA J. Appl. Math., 41, 21-30 (1988) · Zbl 0692.35074
[14] Jones, D. S., An approximate boundary condition in acoustics, J. Sound Vibration, 121, 37-45 (1988) · Zbl 1235.76158
[15] Kohn, J. J.; Nirenberg, L., An algebra of pseudodifferential operators, Comm. Pure Appl. Math., 18, 269-305 (1965) · Zbl 0171.35101
[16] Kriegsmann, G. A.; Taflove, A.; Umashankar, K. R., A new formulation of electromagnetic wave scattering using the on-surface radiation condition approach, IEEE Trans. Antennas and Propagation, 35, 153-161 (1987) · Zbl 0947.78571
[17] Majda, A.; Osher, S., Reflection of singularities at the boundary, Comm. Pure Appl. Math., 28, 479-499 (1975) · Zbl 0307.35077
[18] D. B. Meade, A. F. Peterson, C. Piellusch-Castle, Derivation and comparison of radiation boundary conditions for the two-dimensional Helmholtz equation with non-circular artificial boundaries, in; D. B. Meade, A. F. Peterson, C. Piellusch-Castle, Derivation and comparison of radiation boundary conditions for the two-dimensional Helmholtz equation with non-circular artificial boundaries, in · Zbl 0870.35009
[19] Mittra, R.; Ramahi, O., Absorbing boundary conditions for the direct solution of partial differential equations arising in electromagnetic scattering problems, (Morgan, M. A., Progress in Electromagnetics Research: Finite Element and Finite Difference Methods in Electromagnetic Scattering (1990), Elsevier: Elsevier Newark)
[20] Mur, G., Absorbing boundary conditions for the finite-difference approximation of time-domain electromagnetic field equations, IEEE Trans. Electromagnet. Compat., 23, 377-382 (1981)
[21] Nirenberg, L., Pseudodifferential operators and some applications, Lectures on Linear Partial Differential Equations, CBMS Regional Conf. Ser. in Math., 17, 19-58 (1973)
[22] Stupfel, B., Absorbing boundary conditions on arbitrary boundaries for the scalar and vector wave equations, IEEE Trans. Antennas and Propagation, 42, 773-780 (1994) · Zbl 0953.78500
[23] Taylor, M. E., Pseudodifferential Operators (1981), Princeton Univ. Press: Princeton Univ. Press Princeton · Zbl 0453.47026
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