# Regularity of solutions to Helmholtz-type problems with absorbing boundary conditions in nonsmooth domains

• Kim, Jinsoo (Department of Mathematics, Seoul National University, Seoul 151-742) ;
• Dongwoo Sheen (Department of Mathematics, Seoul National University, Seoul 151-742)
• Published : 1997.02.01

For the numerical simulation of wave phenomena either in unbounded domains that it is not feasible to compute solutions on the entire region, it is needed to truncate the original domains to manageable bounded domains whose geometries are simple but usually nonsmooth. On the artificial boundaries thus created, absorbing boundary conditions are taken so that the significant part of waves arriving at the artificial boundaries can be transmitted [5,10,11,16,17,26]$. #### Keywords #### File #### References 1. Sobolev Spaces R. A. Adams 2. Comm. Pure Appl. Math. v.12 Estimates Near the Boundary for Solutions of Elliptic Partial Differential Equations Satisfying General Boundary Conditions Ⅰ S. Agmon;A. Douglis;L. Nirenberg 3. Comm. Pure Appl. Math. v.17 Estimates Near the Boundary for Solutions of Elliptic Partial Differential Equations Satisfying General Boundary Conditions S. Agmon;A. Douglis;L. Nirenberg 4. Handbook of Numerical Analysis, Finite Element Methods v.Ⅱ P. G. Ciarlet;J. L. Lions 5. Bull. Seis. Soc. Amer. v.67 Absorbiny Boundary Conditions for Acoustic and Elastic, Wave Equations R. Clayton;B. Engquist 6. Lecture Notes in Mathematics 1341 Elliptic Boundary Value Problems on Corner Domains M. Dauge 7. Mathematical Analysis and Numerical Methods for Science and Technology v.1-5 R. Dautray;J. L. Lions 8. Math. Mod. Meth. Appl. Sci. v.4 Approximation of Scalar Waves in the Space-Frequency Domain J. Douglas, Jr.;J. E. Santos;D. Sheen 9. Math. Mod. Meth. Appl. Sci. v.3 Frequency Domain Treatment of One-Dimensional Scalar Waves J. Douglas, Jr.;J. E. Santos;D. Sheen;L. S. Bennethum 10. Math. Comp. v.31 Absorbing Boundary Conditions for the Numerical Simulation of Waves B. Engquist;A. Majda 11. Comm. Pure Appl. Math. v.32 Radiation Boundary Conditions for Acoustic and Elastic Wave Calculations B. Engquist;A. Majda 12. Trans. Amer. Math. Soc. v.346 An Elliptic Regularity Estimate for a Problem Arising from the Frequency Domain Treatment of Waves X. Feng;D. Sheen 13. J. Differential Equations v.15 On the Existence, Uniqueness and Regularity of Solutions to General Elliptic Boundary Value Problems R. S. Freeman;M. Schechter 14. Elliptic Partial Differential Equations of Second Order D. Gilbarg;N. S. Trudinger 15. Elliptic Problems in Nonsmooth Domains P. Grisvard 16. Math. Comp. v.47 Absorbing Boundary Conditions for Difference Approximations to the Multi-Dimensional Wave Equation R. L. Higdon 17. SIAM J. Numer. Anal. v.27 Radiation Boundary Conditions for Elastic Wave Propagation R. L. Higdon 18. Math. USSR-Sb v.3 Traces of Functions in the Space$＼stackrel{l}{p}\$ on Pieceunse Smooth Surfaces G. N. Jakovlev
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