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2001 Fiscal Year Final Research Report Summary

Updating of Poisson Solvers

Research Project

Project/Area Number 10554003
Research Category

Grant-in-Aid for Scientific Research (B)

Allocation TypeSingle-year Grants
Section展開研究
Research Field General mathematics (including Probability theory/Statistical mathematics)
Research InstitutionTHE UNIVERSITY OF ELECTRO-COMMUNICATIONS

Principal Investigator

USHIJIMA Teruo  THE UNIVERSITY OF ELECTRO-COMMUNICATIONS, FACULTY OF ELECTRO-COMMUNICATIONS, PROFESSOR, 電気通信学部, 教授 (10012410)

Co-Investigator(Kenkyū-buntansha) SUGIHARA Masaaki  NAGOYA UNIVERSITY, GRADUATE SCHOOL OF ENGINEERING, PROFESSOR, 大学院・工学研究科, 教授 (80154483)
AMANO Kaname  EHIME UNIVERSITY, FACULTY OF ENGINEERING, PROFESSOR, 工学部, 教授 (80113512)
TABATA Masahisa  KYUSHU UNIVERSITY, GRADUATE SHCOOL OF SCIENCES, PROFESSOR, 大学院・理学研究院, 教授 (30093272)
KAKO Takashi  THE UNIVERSITY OF ELECTRO-COMMUNICATIONS, FACULTY OF ELECTRO-COMMUNICATIONS, PROFESSOR, 電気通信学部, 教授 (30012488)
TAKEDA Tatsuoki  THE UNIVERSITY OF ELECTRO-COMMUNICATIONS, FACULTY OF ELECTRO-COMMUNICATIONS, PROFESSOR, 電気通信学部, 教授 (60272746)
Project Period (FY) 1998 – 2001
KeywordsPoisson solver / fundamental solution method / Finite element method / Numerical conformal mapping / Radiation and scattering problems in infinite domains / Odd and even dimensional Radon transforms / Asymmetric Abel inversion / Numerical methods for Helmholtz equations
Research Abstract

1. Main Results Obtained in the Joint Works around the Head Investigator :
In the computatioin of two dimensional perfect fluid around an air foil through finite element method, setting a sufficiently large disc containing the air foil, let a doubly connected region, which is the intersection of the disc and the complement of the air foil, be our computational domain. Setting a transparent boundary condition on the circular boundary of the computational domain. Setting a transparent boundary condition on the circular boundary of the computational domain, we execute finite element numerical computations for discretized Laplace problems in the domain. To solve the discretized problems, an FEM-CSM (finite Element Method -- Charge Simulation Method) combined method for 2D exterior Laplace problems is proposed and mathematically justified. In this combined method transparent boundary condition is approximated through charge simulation method. For an FSM (Fundamental Solution Method) approxim … More ate problem for Helmholtz equation in the exterior domain of a disc, a unique solvability theorem and an error estimate theorem are obtained in the case of equi-distant equally phased arrangement of source points and collocation points.
2. Remarkable Progress Obtained in the Works by Investigators :
(1) Representations of the inversions of the odd and even dimensional Radon transforms and numerical reconstruction procedures based on them (by J. Watanabe)
(2) Neural network calculation in asymmetric Abel inversion (by T. Takeda and M Fukuhara)
(3) Finite element numerical method based on the domain decomposition method and fictitious domain method applied to radiation and scattering problem in unbounded region (by T. Kako).
(4) fundamental research for numerical simulation of dynamical systems generated by delay differential equations (by T. Koto).
(5) A free boundary problem related to eigenvalue problems for a class of elliptic partial differential operators (by I. Ohnishi).
(6) Theoretical study on reaction-diffusion equations and their singular limits describing the growth of screw dislocation on the crystal surface (by K. Nakamura).
(7) Finite element computations for 3D exterior Helmholtz problem (by D. Koyama).
(8) A parallel computation code for 3D numerical simulation of Earth's mantle convection (by M. Tabata).
(9) Proposal of a method of numerical conformal mappings of unbounded multiply-connected domains onto canonical slit domains using the charge simulation method, and confirmation of its effectiveness by numerical experiments (by K. Amano).
(10) A theoretical study on the 1-dimensional Poisson solvers based on sinc functions (by M. Sugihara).
(11) Mathematical foundation of residual cutting method (by T. Takahashi).
(12)Role of Poisson solvers in bio-informatics (by S. Ihara).
(13) Derivation of basic system of equations for multi phase flow appearing in the structure formation in nanotechnology (by H. Yasuda). Less

  • Research Products

    (71 results)

All Other

All Publications (71 results)

  • [Publications] 牛島照夫, 横松大作: "有限要素計算による翼の等角写像における主要項の決定"数理解析研究所講究録1040「数値計算アルゴリズムの研究」京都大学数理解析研究所. 118-124 (1998)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] TABATA, Masahisa: "A nonconforming finite element approximation to the axisymmetric Poisson problem"Proceedings of Third China-Japan Joint Seminar on Numerical Mathematics, held in Dalian China, August 26-30, 1996, Edited by Z.-C.Shi and M.Mori Science Press, Beijing/New York. 138-147 (1998)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] AMANO, Kaname: "A charge simulation method for numerical conformal mapping onto circular and radial slit domains"SIAM Journal on Scientific Computing. Vol.19,No.4. 1169-1187 (1998)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 劉 小進, 加古 孝: "領域分割法を用いたヘルムホルツ方程式に対する反復解法"日本応用数理学会論文誌. Vol.8,No.4. 435-446 (1998)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] OHNISHI, Isamu, NISHIURA, Yasumasa, IMAI, Masaki, MATSUSHITA, Yushu: "Analytical Solutions describing the phase separation driven by a free energy functional containing a long-range interaction term"CHAOS special issue. Vol.9,No.2. 329-341 (1999)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] NAKAMURA, Ken-iti, MATANO, Hirosi, HILHORST, D., SCHATZ, R: "Singular limit of a reaction-diffusion equation with a spatially inhomogeneous reaction term"Journal of Statistical Physics. Vol.95,Nos.5/6. 1165-1185 (1999)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] D.KOYAMA, K.TANIMOT, T.USHIJIMA: "Finite element analysis for the eigenvalue problem of the linear water wave in a water region with a reentrant corner"Japan Journal of Industrial and Applied Mathematics. Vol.15. 395-422 (1998)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 牛島照夫, 横松大作, 安藤一平, 矢野祐輔: "有限要素計算による翼の等角写像の探究"航空宇宙技術研究所特別資料. SP-41. 297-302 (1999)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] M.Tabata, D.Tagami: "A finite element analysis of a linearized problem of the Navier-Stokes equations with surface tension"SIAM Journal on Numerical Analysis. Vol.38. 40-57 (2000)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Amano, K., Okano, D., Shimohira H., Okamoto, T., Igaue, Y: "Potential flow analysis by the numerical conformal mapping"Information. Vol.3,No.1. 73-88 (2000)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 加古孝, 加納知聡: "定常波動問題にたいする領域分割法とその応用"京都大学数理解析研究所講究録. 1129. 54-59 (2000)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Tatsuoki TAKEDA, Makoto FUKUHARA, Xiao Feng MA, Ali LIAQAT: "Applications of Neural Network to Numerical Analyses"Proceeding of 1998-Workshop on MHD Computations, "Study on Numerical Methods Related to Plasma Confinement". 19-29 (1999)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Toshiko Ogiwara, K.-I.Nakamura: "Spiral traveling wave solutions of some parabolic equations on annuli"Josai Mathematical Monographs. Vol.2. 15-34 (2000)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] USHIJIMA, Teruo: "FEM-FSM combined method for 2D exterior Laplace and Helmholtz problems"Proceedings of DD12, 12th International Conference on Domain Decomposition Methods, Chiba, Japan, October 25-29, 1999. 223-230 (2001)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] USHIJIMA, Teruo: "An FEM-CSM combined method for planar exterior Laplace problems"Japan Journal of industrial and Applied Mathematics. Vol.18,No,2. 359-382 (2001)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 牛島照夫, 増田 茂: "二次元外部ラプラスならびにヘルムホルツ問題に対するFEM-FSM結合解法"核融合科学研究所 研究レポート. NIFS-PROC-46. 165-174 (2000)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] M.Tabata, D.Tagami: "Error estimates for finite element approximations of drag and lift in nonstationary Navier-Stokes flows"Japan Journal of Industrial and Applied Mathematics. Vol.17. 371-389 (2000)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 天野 要, 岡野 大, 緒方秀教: "代用電荷法による円弧スリット単位円板領域への数値等角写像の方法"情報処理学会論文誌. Vol.41,No.4. 998-1008 (2000)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Zhang.S.-L., Oyanagi, Y., Sugihara, M.: "Necessary and Sufficient Conditions for the Convergence of Orthomin(k) on Singular and Inconsistent Linear Sysytems"Numerische Mathematik. Vol.87. 391-405 (2000)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] KAKO, Takashi, KANO, Tomotoshi, LI Xiao-Jin, YAMASHITA, Takehik: "Domain decomposition method applied to radiation problems"Proceedings of 12th DDM International Conference. 381-392 (2001)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 馬笑峰, 竹田辰興: 日本応用数理学会論文誌. 第10巻、第2号. 145-161 (2000)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Xiao Feng Ma, Makoto Fukuhara, Tatsuoki Takeda: "Neural network CT image reconstruction method for small amount of projection data"Nuclear instruments and Methods in Physics Research A. 449. 366-377 (2000)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 彌政敦洋, 竹田辰興, 中村一男, 伊藤智之: "TRIAM-1Mにおけるフィードバック制御に用いるニューラルネットワークの構造最適化"プラズマ・核融合学会誌. 第76巻、第9号. 911-921 (2000)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Sagun Chanillo, Daniel Grieser, Masaki Imai, Kazuhiro Kurata, Isamu Ohnishi: "Symmetry Breaking and Other Phenomena in the Optimization of Eigenvalues for composite Membranes"Communications in Mathematical Physics. 214巻. 315-337 (2000)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Toshiyuki Koto: "Periodic orbits in the Euler method for a class of delay differential equations"Comput. Math. Appl.. Vol.42. 1597-1608 (2001)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] M.Tabata: "Uniform solvability of finite element solutions in approximate domains"Japan Journal of Industrial and Applied Mathematics. Vol.18. 567-585 (2001)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Y.Mizuyama, M.Tabata.: "Lagrangian finite element analysis of the free surface of anincompressible dielectric liquid under an electric field"Theoretical Applied Mechanics. Vol.50. 403-412 (2001)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] M.Tabata, S.Fujima: "Numerical analysis of flow problems by finite element methods"Sugaku Expositions. Vol.14. 155-174 (2001)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] M.Tabata, A.Suzuki: "Mathematical modeling and numerical simulation of Earths mantle convection"Mathematical Modeling and Numerical Simulation in Continuum Mechanics, Lecture Notes in Computational Science and Engineering. Vol.19. 219-231 (2001)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] H.Rui, M.Tabata: "A second order characteristic finite element scheme for convection-diffusion problems"Numerische Mathematik. (to appear). (2002)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 岡野 大, 牧 直正, 緒方秀教, 天野 要: "代用電荷法による円弧スリット円環領域への数値等角写像の方法"情報処理学会論文誌. (to appear). (2002)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Okano, D., Ogata, H., Amano, K.: "Stagnation point analysis by the numerical conformal mapping using the charge simulation method"Theoretical and Applied Mechanics. Vol.50. 303-309 (2001)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Ogata, H., Okano, D., Amano, K.: "Numerical conformal mapping of periodic structure domains"Proceeding of the Eighth International Conference on Finite or Infinite Dimensional Complex Analysis. 175-182 (2001)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] M.Mori, M.Sugihara: "The Double Exponential Transformation in Numerical Analysis"Numerical Analysis in the 20th Century Vol.V : Quadrature and Orthogonal Polynomials, Journal of Computational and Applied Mathematics. Vol.127. 287-296 (2001)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 影山康夫, 杉原正顯: "代用電荷法に基づく補間法に現れる係数行列の正則性"日本応用数理学会論文誌. Vol.11. 171-177 (2001)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] M.Sugihara: "Near-optimality of the Sinc approximation"Mathematics of Computation. (to appear).

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Ali Liaqat, Makoto Fukuhara, Tatsuoki Takeda: "Application of neural network collocation method to data assimilation"Computer Physics Communications. 141. 350-364 (2001)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] NASIR, H.Mohamed, KAKO, Takashi: "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(和文)」より
  • [Publications] KAKO, Takashi, NASIR, H. Mohamed: Lecture Notes in Computational Science and Engineering, Mathematical Modeling and Numerical Simulation in Continuum Mechanics, Proceedings of International Symposium on Mathematical Modeling and Numerical Simulation in Continuum Mechanics. Vol.19. 155-167 (2002)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 大西 勇, 今井正城, 西浦廉政: "エネルギー最小化の視点からの、空間1次元のActivator-Inhibitor systemの最安定定常解"京都大学数理解析研究所講究録. 1216. 45-50 (2001)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Toshiko Ogiwara, Ken-Ichi Nakamura: "Asymptotic behavior of solutions to a model of spiral crystal growth"京都大学数理解析研究所講究録. (to appear). (2002)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] TABATA, Masahisa: "A nonconforming finite element approximation to the axisymmetric Poisson problem"Proceedings of Third China-Japan Joint Seminar on Numerical Mathmatics, held in Dalian Chi August 26-30, 1996, Edited by Z.-C. Shi and M. Mori, Science Press, Beijing/New York. 138-1247 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] AMANO, Kaname: "Charge simulation method for numerical conformal mapping onto circular and radial slit domains"SIAM Journal on Scientific Computing. Vol.19,No.4. 1169-1187 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] OHNISHI, Isamu, NISHIURA, Yasumasa, IMAI, Masaki and MATSUSHITA, Yushu: "Analytical Solutions describing the phase separation driven by a free energy functional containing a long-range interactiion term"CHAOS. Vol.9,No.2. 329-341 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] NAKAMURA, Ken-iti, MATANO, Hirosi, HILHORST, D., SCHATZ, R.: "Singular limit of a reaction-diffusion equation with a spatially inhomogeneous reaction term"Jourrnal of Statistical Physics. Vol.95,Nos.5/6. 1165-1185 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] D. Koyama, K. Tanimoto and T. Ushijima: "Finite element analysis for the eigenvalue problem of the linear water wave in a water region with a reentrant corner"Japan Journal of Industrial and applied Mathematics. Vol.15. 395-422 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] M. Tabata and D. Tagami: "A finite element analysis fo a linearized problem of the Navier-Stokes equations with surface tension"SIAM Journal on Numerical Analysis. Vol.38. 40-57 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Amano, K., Okano, D., Shimohira, H., Okamoto, T. and Igaue, Y.: "Potential flow analysis by the numerical conformal mapping"Information. Vol.3,No.1. 73-88 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Tatsuoki TAKEDA, Makoto FUKUHARA, Xiao Feng MA, and Ali LIAQAT: "Applications of Neural Network to Numerical Analyse"Proceeding of 1998-Workshop on MHD Computations, "Study on Numerical Methods Related to Plasma Confinement". 19-29 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Toshiko Ogiwara and Ken-Ichi Nakamura: "Spiral traveling wave solutions of some parabolic equations on annul"Josai Mathematical Monographs. Vol.2. 15-34 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] USHIJIMA, Teruo: "FEM-FSM combined method for 2D exterior Laplace and Helmholtz problems"Proceedings of 12th International Conference on Domain Decomposition Methods, Chiba, Japan, October 25-29, 1999, Edited by T. Chan, T. Kako, H. Kawarada and O. Pironneau DDM. org. Printed in Japan. 223-230 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] USHIJIMA, Teruo: "An FEM-CSM combined method for planar exterior Laplace problems"Japan Journal of Industrial and Applied Mathematics. Vol.18,No.2. 359-382 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] M. Tabata and D. Tagami: "Error estimates for finite element approximations of drag and lift in nonstationary Navier-Stokes flows"Japan Journal of Industrial and Applied Mathematics. Vol.17. 371-389 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Zhang, S.-L., Oyanagi, Y. and Sugihara, M.: "Necessary and sufficient conditions for the convergence of orthomin(k) on singular and inconsistent linear systems"Numerische Mathematik. Vol.i87. 391-405 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] KAKO, Takashi, KANO, Tomotoshi, LIU, Xiao-Jin, and YAMASHITA, Takehiko: "Domain decomposition method applied to radiation problems"Proceedings of 12th International Conference on Domain Decomposition Methods, Chiba, Japan, October 25-29, 1999, Edited by T. Chan, T. Kako, H. Kawarada and O. Pironneau, DDm. org, Printed in Japan. (2001)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Xiao Feng Ma, Makoto Fukuhara, Tatsuoki Takeda: "Neural network CT image rfeconstruction method for small amount of projection data"Nuclear Instruments and Methods in Physics Research A. Vol.449. 366-377 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Sagun Chanillo, Daniel Grieser, Masaki Imai, Kazuhiro Kurata, Isamu Ohnishi: "P+eriodic orbits in the Euler method for a class of delay differential equations"Communications in Mathematical Physics. Vol.214. 315-337 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Toshiyuki Koto: "Periodic orbitts in the Euler method for a class of delay differential equations"Comput. Math. Appl.. Vol.42. 1597-1608 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] M. Tabata: "Uniform solvability of finite elemenet solujtiions in approximatedomains"Japan Journal of Industrial and Applied Mathematics. Vol.18. 567-585 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Y. Mizuyama and M. Tabata: "Lagrangian finite element analysis of the free surface of an incompressible dielectric liquid under an electric field"Theoretical Applied Mechanics. Vol.50. 403-410 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] M. Tabata and S. Fujima: "Numerical analysis of flow problems by finite element methods"Sugaku Expositions. Vol.14. 155-174 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] H. Rui and M. Tabata: "A second order characteristic finite element scheme for convection-diffusion problems"Numerische Mathematik. (to appear). (2002)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Okano, D., Ogata, H. and Amano, K.: "Stagnation point analysis by the numerical conformal mapping using the charge simulation method"Theoretical and Applied Mechanics, Hokusensha, Tokyo. Vol.50. 303-309 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Ogata, H., Okano, D. and Amano, K.: "Numerical conformal mapping of periodic structure domains"Proceeding of the Eighth International Conferenced on Finite or Infinite Dimensional Complex Analysis, Shandong Science and Technology Press. 175-182 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] M. Mori, and M. Sugihara: "The Double Exponential Transformation in Numerical Analysis"Numerical Analysis in the 20th Century Vol.V : Quadrature and Orthogonal Polynomials, Journal of Computational and Applied Mathematics. Vol.127. 287-296 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] M. Sugihara: "Near-optimality of the Sinc approximation"Mathematics of Computation. (to appear).

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Ali Liaqat, Makoto fukuhara, Tatsuoki Takeda: "Application of neural network collocation method to data assimilation"Computer Physics Communications. Vol.141. 350-364 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] NASIR, H. Mohamed and KAKO, Takashi: "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, Takashi and NASIR, H. Mohamed: "Essential spectrum and mixed type finite element method"Lecture Notes in Computational Science and Engineering, Mathematical Modeling and Numerical Simulation in Continuum Mechanics, Proceedings of International Symposium on Mathematical Modeling and Numerical Simulation in Cotinuum Mechanics. Vol.19. 155-167 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Toshiko Ogiwara and Ken-Ichi Nakamura: "Asymptotic behavior of solutions to model of spiral crystal growth"SUURIKAISEKI KOUKYUUROKU. (to appear). (2002)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] M. Tabata and A. Suzuki: "Mathematical modeling and numerical simulation of Earth's smantle convection, In P.G. Ciarlet I. Babuska and T. Miyoshi, editors, Mathematical Modeling and Numerical Simulation in Continuum Mechanics, Vol.19 of Lecture Notes in Computational Science and Engineering"Springer, Berlin. 219-231 (2001)

    • 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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