Lee, Chang-Ock; Lee, Jongwoo; Sheen, Dongwoo; Yeom, Yongjin A frequency-domain parallel method for the numerical approximation of parabolic problems. (English) Zbl 0946.65094 Comput. Methods Appl. Mech. Eng. 169, No. 1-2, 19-29 (1999). Solution method for parabolic equations by going with Fourier transform in time to the frequency domain. For each frequency then an independent elliptic problem must be solved. The theory of the method including error estimates is presented. An example on 12 processors (72 frequencies) shows excellent speedup. However, the main question, if this method is more efficient than usual high-order finite difference methods, is not discussed. Reviewer: W.Schönauer (Karlsruhe) Cited in 4 Documents MSC: 65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs 65Y05 Parallel numerical computation 65M15 Error bounds for initial value and initial-boundary value problems involving PDEs 35K15 Initial value problems for second-order parabolic equations Keywords:parabolic equations; time-frequencies transformation; parallel computing; Fourier transform method; error estimates Software:YSMP PDF BibTeX XML Cite \textit{C.-O. Lee} et al., Comput. Methods Appl. Mech. Eng. 169, No. 1--2, 19--29 (1999; Zbl 0946.65094) Full Text: DOI OpenURL References: [1] Adams, R.A., Sobolev spaces, (1975), Academic Press Englewood Cliffs, NJ · Zbl 0186.19101 [2] Cok, R.S., Parallel programs for the transputer, (1991), Prentice-Hall, Inc. London [3] Dautray, R.; Lions, J.-L., () [4] Douglas, J.; Santos, J.E.; Sheen, D., Approximation of scalar waves in the space—frequency domain, Math. model methods appl. sci., 4, 509-531, (1994) · Zbl 0812.35173 [5] Douglas, J.; Santos, J.E.; Sheen, D.; Bennethum, L.S., Frequency domain treatment of one-dimensional scalar waves, Math. model methods appl. sci., 3, 171-194, (1993) · Zbl 0783.65070 [6] Eisenstat, S.C.; Elman, H.E.; Schultz, M.H.; Sherman, A.H., The (new) yale sparse matrix package, (), 45-52 [7] Feng, X.; Sheen, D., An elliptic regularity estimate for a problem arising from the frequency domain treatment of waves, Trans. am. math. soc., 346, 475-487, (1994) · Zbl 0811.35021 [8] Gilbarg, D.; Trudinger, N.S., Elliptic partial differential equations of second order, (1983), Springer-Verlag New York · Zbl 0691.35001 [9] Grisvard, P., Boundary value problems in non—smooth domains, (1985), Pitman Berlin, Heidelberg · Zbl 0695.35060 [10] Kim, D.; Kim, J.; Sheen, D., Absorbing boundary conditions for wave propagations in viscoelastic media, J. comput. appl. math., 76, 301-314, (1995) · Zbl 0864.73020 [11] Kim, J.; Sheen, D., An elliptic regularity of a Helmholtz-type problem with an absorbing boundary condition, Bull. Korean math. soc., 34, 135-146, (1997) · Zbl 0890.35018 [12] Lawson, H.W., Parallel processing in industrial real-time applications, (1992), Prentice-Hall, Inc. Boston, London [13] Lee, C.-O.; Lee, J.; Sheen, D., A frequency-domain method for finite element solutions of parabolic problem, () [14] Lee, C.-O.; Lee, J.; Sheen, D., Frequency domain formulation of linearized navier—stokes equations, () · Zbl 0952.76065 [15] Lions, J.L., Quelques Méthodes de resolution des problémes aux limites non lińeaires, (1969), Dunod Gauthier-Villars Seoul 151-742, Korea · Zbl 0189.40603 [16] Nečas, J., LES Méthodes directes en theorie des equations elliptiques, (1967), Masson Paris · Zbl 1225.35003 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.