메뉴 건너뛰기




Volumn 85, Issue 3, 2011, Pages 380-402

A comparison of wave-based discontinuous Galerkin, ultra-weak and least-square methods for wave problems

Author keywords

Discontinuous Galerkin; Helmholtz; Least square; Ultra weak

Indexed keywords

COMMON FEATURES; DISCONTINUOUS GALERKIN; DISCONTINUOUS GALERKIN METHODS; HELMHOLTZ; HIGH FREQUENCY; INTERPOLATION ERROR; LEAST SQUARE; LEAST SQUARE METHODS; LEAST SQUARES METHODS; LOCAL SOLUTION; MATCHING CONDITION; NUMBER OF DEGREES OF FREEDOM; NUMERICAL ACCURACY; NUMERICAL FLUX; NUMERICAL RESULTS; POLYNOMIAL INTERPOLATION; POLYNOMIAL METHODS; RELATIVE ACCURACY; TREFFTZ METHODS; ULTRA-WEAK; UNIFIED FRAMEWORK; VARIATIONAL FORMULATION; WAVE PROBLEMS; WAVE PROPAGATION PROBLEMS;

EID: 78650551182     PISSN: 00295981     EISSN: 10970207     Source Type: Journal    
DOI: 10.1002/nme.2979     Document Type: Article
Times cited : (32)

References (30)
  • 1
    • 78650552697 scopus 로고
    • On generalized finite element methods. Ph.D. Thesis, University of Maryland.
    • Melenk JM. On generalized finite element methods. Ph.D. Thesis, University of Maryland, 1995.
    • (1995)
    • Melenk, J.M.1
  • 6
    • 39749162843 scopus 로고    scopus 로고
    • A discontinuous enrichment method for capturing evanescent waves in multiscale fluid and fluid/solid problems
    • Tezaur R, Zhang L, Farhat C. A discontinuous enrichment method for capturing evanescent waves in multiscale fluid and fluid/solid problems. CMAME 2008; 197:1680-1898.
    • (2008) CMAME , vol.197 , pp. 1680-1898
    • Tezaur, R.1    Zhang, L.2    Farhat, C.3
  • 7
    • 57849165439 scopus 로고    scopus 로고
    • A discontinuous enrichment method for three-dimensional multiscale harmonic wave propagation problems in multi-fluid and fluid-solid media
    • Massimi P, Tezaur R, Farhat C. A discontinuous enrichment method for three-dimensional multiscale harmonic wave propagation problems in multi-fluid and fluid-solid media. International Journal for Numerical Methods in Engineering 2008; 76:400-425.
    • (2008) International Journal for Numerical Methods in Engineering , vol.76 , pp. 400-425
    • Massimi, P.1    Tezaur, R.2    Farhat, C.3
  • 8
    • 0037436501 scopus 로고    scopus 로고
    • A discontinuous Galerkin method with Lagrange multipliers for the solution of Helmholtz problems in the mid-frequency regime
    • Farhat C, Harari I, Hetmaniuk U. A discontinuous Galerkin method with Lagrange multipliers for the solution of Helmholtz problems in the mid-frequency regime. Computer Methods in Applied Mechanics and Engineering 2003; 192:1389-1419.
    • (2003) Computer Methods in Applied Mechanics and Engineering , vol.192 , pp. 1389-1419
    • Farhat, C.1    Harari, I.2    Hetmaniuk, U.3
  • 10
    • 1642369052 scopus 로고    scopus 로고
    • A discontinuous Galerkin method with plane waves and Lagrange multipliers for the solution of short-wave Helmholtz problems on unstructured meshes
    • Farhat C, Weidemann-Goiran P, Tezaur R. A discontinuous Galerkin method with plane waves and Lagrange multipliers for the solution of short-wave Helmholtz problems on unstructured meshes. Wave Motion 2004; 39:307-317.
    • (2004) Wave Motion , vol.39 , pp. 307-317
    • Farhat, C.1    Weidemann-Goiran, P.2    Tezaur, R.3
  • 11
    • 0141445578 scopus 로고    scopus 로고
    • Application of an ultra weak variational formulation of elliptic PDEs to the two-dimensional Helmholtz problem
    • Cessenat O, Després B. Application of an ultra weak variational formulation of elliptic PDEs to the two-dimensional Helmholtz problem. SIAM Journal on Numerical Analysis 1998; 35:255-299.
    • (1998) SIAM Journal on Numerical Analysis , vol.35 , pp. 255-299
    • Cessenat, O.1    Després, B.2
  • 14
    • 34547552637 scopus 로고    scopus 로고
    • Discontinuous Galerkin methods with plane waves for time-harmonic problems
    • Gabard G. Discontinuous Galerkin methods with plane waves for time-harmonic problems. Journal of Computational Physics 2007; 225:1961-1984.
    • (2007) Journal of Computational Physics , vol.225 , pp. 1961-1984
    • Gabard, G.1
  • 15
    • 34547106039 scopus 로고    scopus 로고
    • A comparison of two Trefftz-type methods: the ultraweak variational formulation and the least-squares method, for solving shortwave 2-D Helmholtz problems
    • Gamallo P, Astley RJ. A comparison of two Trefftz-type methods: the ultraweak variational formulation and the least-squares method, for solving shortwave 2-D Helmholtz problems. International Journal for Numerical Methods in Engineering 2007; 71:406-432.
    • (2007) International Journal for Numerical Methods in Engineering , vol.71 , pp. 406-432
    • Gamallo, P.1    Astley, R.J.2
  • 20
    • 64049102865 scopus 로고    scopus 로고
    • Numerical modelling of elastic wave scattering in frequency domain by the partition of unity finite element method
    • El Kacimi A, Laghrouche O. Numerical modelling of elastic wave scattering in frequency domain by the partition of unity finite element method. International Journal for Numerical Methods in Engineering 2009; 77:1646-1669.
    • (2009) International Journal for Numerical Methods in Engineering , vol.77 , pp. 1646-1669
    • El Kacimi, A.1    Laghrouche, O.2
  • 21
    • 33947105064 scopus 로고    scopus 로고
    • Solving Maxwell's equations using the ultra weak variational formulation
    • Huttunen T, Malinen M, Monk P. Solving Maxwell's equations using the ultra weak variational formulation. Journal of Computational Physics 2007; 223:731-758.
    • (2007) Journal of Computational Physics , vol.223 , pp. 731-758
    • Huttunen, T.1    Malinen, M.2    Monk, P.3
  • 24
    • 30644469853 scopus 로고    scopus 로고
    • The partition of unity finite element method for short wave acoustic propagation on non-uniform potential flows
    • Gamallo P, Astley RJ. The partition of unity finite element method for short wave acoustic propagation on non-uniform potential flows. International Journal for Numerical Methods in Engineering 2006; 65:425-444.
    • (2006) International Journal for Numerical Methods in Engineering , vol.65 , pp. 425-444
    • Gamallo, P.1    Astley, R.J.2
  • 25
    • 0003733595 scopus 로고    scopus 로고
    • Finite Volume Methods for Hyperbolic Problems
    • Cambridge University Press: Cambridge.
    • Leveque RJ. Finite Volume Methods for Hyperbolic Problems. Cambridge University Press: Cambridge, 2002.
    • (2002)
    • Leveque, R.J.1
  • 26
    • 84889809594 scopus 로고    scopus 로고
    • Riemann Solvers and Numerical Methods for Fluid Dynamics: A Practical Introduction
    • Springer: Berlin.
    • Toro EF. Riemann Solvers and Numerical Methods for Fluid Dynamics: A Practical Introduction. Springer: Berlin, 1999.
    • (1999)
    • Toro, E.F.1
  • 28
    • 0022728049 scopus 로고
    • Initial-boundary value problems for linear hyperbolic systems
    • Higdon RL. Initial-boundary value problems for linear hyperbolic systems. SIAM Review 1986; 28(2):177-217.
    • (1986) SIAM Review , vol.28 , Issue.2 , pp. 177-217
    • Higdon, R.L.1
  • 29
    • 17444409296 scopus 로고    scopus 로고
    • A discontinuous Galerkin method for linear symmetric hyperbolic systems in inhomogeneous media
    • Monk P, Richter GR. A discontinuous Galerkin method for linear symmetric hyperbolic systems in inhomogeneous media. Journal of Scientific Computing 2005; 22:443-477.
    • (2005) Journal of Scientific Computing , vol.22 , pp. 443-477
    • Monk, P.1    Richter, G.R.2
  • 30
    • 2342498610 scopus 로고    scopus 로고
    • Estimates in the fast multipole method for scattering problems part 1: truncation of the Jacobi-Anger series
    • Carayol Q, Collino F. Estimates in the fast multipole method for scattering problems part 1: truncation of the Jacobi-Anger series. ESAIM: Mathematical Modeling and Numerical Analysis 2004; 38(2):371-394.
    • (2004) ESAIM: Mathematical Modeling and Numerical Analysis , vol.38 , Issue.2 , pp. 371-394
    • Carayol, Q.1    Collino, F.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.