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2001 Fiscal Year Final Research Report Summary

Study on non-standard finite element approximation methods for partial differential equations

Research Project

Project/Area Number 11440027
Research Category

Grant-in-Aid for Scientific Research (B)

Allocation TypeSingle-year Grants
Section一般
Research Field General mathematics (including Probability theory/Statistical mathematics)
Research InstitutionThe University of Electro-Communications

Principal Investigator

KAKO Takashi  The University of Electro-Communications, Faculty of Electro-communications, Professor, 電気通信学部, 教授 (30012488)

Co-Investigator(Kenkyū-buntansha) TABATA Masahisa  Kyushu University, Faculty of Mathematics, Professor, 大学院・数理学研究科, 教授 (30093272)
KAWARADA Hideo  Chiba University, Faculty of Engineering, Professor, 工学部, 教授 (90010793)
OHTSUKA Koji  Hiroshima Kokusai Gakuin University, Faculty of Engineering, Professor, 工学部, 教授 (30141683)
ZHANG Shao-liang  The University of Tokyo, Graduate School of Engineering, Associate Professor, 大学院・工学系研究科, 助教授 (20252273)
NAKAO Mitushiro  Kyushu University, Faculty of Mathematics, Professor, 大学院・数理学研究科, 教授 (10136418)
Project Period (FY) 1999 – 2001
KeywordsFinite element method / Radiation and scattering problem / Domain decomposition method / Drichlet to Neumann mapping / Fundamental solution method / Earth mantle current / Neutral net computation / Validated computation
Research Abstract

The following results have been obtained for the non-standard finite element method (FEM) and related problems. The head investigator T. Kako studied the wave propagation in the I exterior unbounded region finding the non-standard finite element approximation method j for a non-local Dirichlet to Neumann mapping, and developed an effective method for 2D radiation problem with high wave number. As an application of the method, it has become possible to compute the formant curve close to the one for the real vowels. He developed the numerical method for the coupling problem between the acoustic field and the structure like shell. He also made clear the importance of the essential Spectrum of the operator in its FEM. The followings are the results by investigators. T. Ushijima studied the fundamental solution method for the 2D reduced wave problem and obtained the convergence and the error estimation. K. Houlka developed the Freeform+ project. H. Kawakawa studied the oil adherence and pen … More etration phenomena on the seashore and obtained its mathematical model and did numerical simulations with various applications.F. Kikuchi developed a new FEM for the plate-bending problem with several numerical examples and studied the efficiency of the Nedelec edge element. D. Koyama studied FEM for the 3D exterior Helmholtz problem combining the fictitious domain method and the Schwarz alternative method. T. Takeda and M. Fukuhara developed the structured neural network method for partial differential equations. M. Tabata found the new FEM scheme for earth mantle convection problem with error estimation. S. -L. Zhang studied various conjugate gradient type method for linear equations. T. Miyoshi found a criterion to determine the direction of a crack extension. M. Nakao and N. Yamamoto studied the validated numerical method for FEM computation and developed the method to evaluate the approximation property of FEM with validation by reducing the problem to the generalized matrix eigenvalue problem. Less

  • Research Products

    (24 results)

All Other

All Publications (24 results)

  • [Publications] KAKO, T., KANO, T., LIU, X.-J., YAMASHITA, T.: "Domain decomposition method applied to radiation problems"Proceedings of 12th DDM International Conference, DDM.org. 381-392 (2001)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] NASIR, H.M., KAKO, T.: "Fictitious domain method for structural-acoustic coupling problem in unbounded region"Theoretical and Applied Mechanics. 50. 391-401 (2001)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] KAKO, T., NASIR, H.M.: "Essential spectrum and mixed type finite element method"Lecture Notes in Computational Science and Engineering, Proceedings of MSCOM. 19. 155-167 (2002)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 牛島照夫: "二次元外部ラプラス問題のFEM-CSM近似解の誤差評価"京都大学数理解析研究所講究録. 1198. 122-127 (2001)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Ushijima, T.: "FEM-FSM combined method for 2D exterior Laplace and Helmholtz problems"Proceedings of 12th International Conference on Domain Decomposition Methods, DDM.org. 223-230 (2001)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Ohtsuka, K.: "Theoretical and numerical analysis on 3-dimensional brittle fracture"Lecture Notes in Computational Science and Engineering. 19. 233-251 (2001)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Chan, T., Kako, T., Kawarada, H., Pironneau, O.(Ed.): "Proceedings of 12th International Conference on Domain Decomposition Methods"DDM.org. 453 (2001)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] KAKO, T. and NASIR, H.M.: "Essential spectruma nd mixed type finite element method"Lecture Notes in Computational Science and Engineering, Proceedings of MSCOM. Vol.19. 155-167 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] KAKO, T., KANO, T., LIU, X.-J. and YAMASHITA, T.: "Domain decomposition method applied to radiation problems"Proceedings of 12th DDM International Conference DDM. org.. 381-392 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] NASIR, H.M. and KAKO, T.: "Fictitious domain method for structural-acoustic coupling problem in unbounded region"Theoretical and Applied Mechanics. Vol.50. 391-401 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Kako, T. and Kano, T.: "Finite element method for the Helmholtz equation and numerical simulation of the wave propagation in vocal tract"GAKUTO International Series, Mathematical Sciences and Applications, Advances in numerical mathematics. Vol.12. 55-65 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Ushijima, T.: "FEM-FSM combined method for 2D exterior Laplace and Helmholtz problems"Proceedings of 12th DDM International Conference, DDM. org. 223-230 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Ohtsuka, K.: "Theoretical and numerical analysis on 3-dimensional brittle fracture"Lecture Notes in Computational Science and Engineering. Vol.19. 233-251 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Kikuchi, F.: "Theoretical analysis of Nedelec's edge elements"Japan Journal of Industrial and Applied Mathematics. Vol.18. 321-333 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Suito, H. and Kawarada, H.: "Shape Optimization for an acoustic problem"Proceedings of 12th DDM International Conference, DDM. org. 445-45t3 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Nakao, M.T. and Yamamoto, N.: "A guaranteed bound of the optimal constant in the error estimates for linear triangular element"Computing. Vol.15. 165-173 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Nakao, M.T., Yamamoto, N. and Nagatou, K.: "Numerical verificatiions of eigenvalues of second-order elliptic operators"Japan Journal of Industgrial and Applied Mathematics. Vol.16. 307-320 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Tabata, T. and Suzuki, A.: "Mathematical modeling and numerical simulation of Earth's mantle convection"Lecture Notes in Computational Science and Engineering. Vol.19. 219-231 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Suzuki, A., Tabata, M. and Honda, S.: "Numerical solution of an unsteady earth's mantle convection porblem by a stabilized finite element method"Theoretical and Applied Mechanics. Vol.48. 371-378 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Tabata, M. and Tagami, D.: "A finite elemnet analysis of a linearized problem of the Navier-Stokes equations with surface tension"SIAM Journal on Numerical Analysis. Vol.38. 387-402 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Ma, X.-F., Fukuhara, M. and Takeda, T.: "Neural network CT image reconstruction method for small amount of projection data"Nuclear Instruments and Methods in Physics Research. Vol.A449. 355-377 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Miyoshi, T.: "Direction and curvature of the cracks in two-dimensional elastic bodies"Japan Journal of Industrial and Applied Mathematics. Vol.12. 295-307 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Zhang, S.-L., Wang, R.-H., Oyanagi Y. and Li, W.: "A Kind of Bivariate Cubic Splines and Related Linear Operators on Type-1 Triangulation"Japan Journal of Industrial and Applied Mathematics. Vol.17. 391-402 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Minamoto, T., Yamamoto, N. and Nakao, M.T.: "Numerical verification method for solutions of the perturbed Geliand equation"Methods and Applications of Analysis. Vol.7. 251-262 (2000)

    • Description
      「研究成果報告書概要(欧文)」より

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Published: 2003-09-17  

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