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Parallel finite element method calculation system achieved

Foreign code F110004966
File No. Q98A1-01KR
Posted date Jul 28, 2011
Country Republic of Korea
Application number 20037014753
Gazette No. 20040016863
Gazette No. 100836998
Date of filing Nov 13, 2003
Gazette Date Feb 25, 2004
Gazette Date Jun 10, 2008
International application number JP2002004617
International publication number WO2000093412
Date of international filing May 13, 2002
Date of international publication Nov 21, 2002
Priority data
  • 2002JP04617 (May 13, 2002) WO
  • P2001-142949 (May 14, 2001) JP
Title Parallel finite element method calculation system achieved
Abstract Known examples of methods for solving an ultra large scale structure problem include the domain decomposing method (DDM), the DDM with the Neumann preprocessing, the BDD method, and the parallel CG method. However, there have been problems that the solutions diverge and are not determined, and the time required to solve the ultra large scale structure problem is very long. A parallel infinite element method calculate system for solving the ultra large scale structure problem having degrees of freedom of more than one million, according to the invention, comprises means for decomposing a domain, means for distributing subdomains to portions which the processors cover, means for creating a rigidity matrix, means for setting the subdomain overall superimposition motion, means for initially setting the projection CG method with preprocessings for the all degrees of freedom, means for carrying out recursive calculation by the projection CG method with preprocessings for all the degrees of freedom, and means for outputting the displacement solution.
(C) KIPO WIPO 2007
Outline of related art and contending technology BACKGROUND ART
Structural issues are commonly handled as follows. First, the structure of interest is qualified as a continuous body, and the motion equation (balance equation in the case of static problem) of the continuous body is determined. This equation cannot be loosened strictly in most cases, and cannot be interpreted numerically. To this end, discrete approximate re-shaping of the continuum problem is needed. As one of the methods, the finite element method (I Finite Element Method Structures) Japanese Machine Line 1998). In a finite element method, a spatial region occupied by a continuous body is first divided into a plurality of elements (elements of the finite element method), a function (shape function) in which a region having a non-zero value is localized is introduced into each element, and a displacement field of the continuous body and a motion equation (or a balance equation) thereof are discretized by an approximation in which the displacement field is limited to those expressed by superposition of these functions. By this discretization, the equation results in one (in the case of a static linear problem) or a plurality (e.g., increment step in the case of a non-linear problem, time step in the case of a dynamic problem) of linear equations. The number of degrees of freedom (dimensions) handled by the linear equation is varied by the number of divisions of the element division of the continuous body region by the finite element method, and generally increasing the number of divisions in order to make the approximation good increases the number of degrees of freedom and increases the difficulty of solving the corresponding linear equation.
The static structure problem of micro-deformation results in a linear problem on the finite dimensional dot product vector space V, such as Equation 1, in the finite element method.
Where VIs a space of an allowable displacement field (a vector field satisfying a boundary condition of the displacement field), KIs VDimension of dimVA differential stiffness matrix (corrective value symmetry), uIs VA variable vector of FIs the definition vector of < scan representing external force; page 2 13 line >. VDimension of dimVIs equal to the number of degrees of freedom in question. V Where Equation 1 uIs a problem with solves.
First, the Conjugate Projected Gradient Algorithm (CPG) based on the present disclosure is described in C.Farhat F.-X. Roux: It Parallel Processing in Structural Mechanics, Computational Mechanics Advances 2,1-124, 1994). Generally, the finite dimension dot product vector space V Equation 2, linear equation of phase
Can be considered. KIs the correction-value symmetric linear transform. VPartial space of YOne is selected. VTo YFurnace K-Orthographic projection K-Orthogonal projector P(Y),. are uniquely determined. Is P(Y). Also, the conditions P(Y)+P(a)=1 K-Orthogonal projector P(a)(P(Y)Each of the plurality of display blocks is uniquely determined so that all of the plurality of display blocks of the plurality of display blocks correspond to the respective display blocks of the plurality of display blocks in the entire space VIs P(Y)And P(a)Image space of Y, V(a)3 and K-Orthogonal rectilinear decomposition is performed.
Scope of claims [claim1]
1. A parallel finite element method calculation system that solves a super-large structure problem with a degree of freedom of 1,000,000 or more, the parallel finite element method calculation system comprising:
Means for performing region division,
Means for distributing the partial area to the part in charge of each processor,
Means for creating a stiffness matrix,
Means for setting an overall overlapping movement of the partial region,
Means for performing initial setting of a pre-processed projection CG method of the entire degree of freedom,
Means for iterative calculation of the pre-processed projection CG method of the overall degree of freedom, and
Means for outputting a displacement solution
And a parallel finite element method calculation unit configured to calculate a parallel finite element method for each of the plurality of finite element methods.

[claim2]
2. The method of claim 1, further comprising:
Wherein the means for setting the overlap motion of the entire partial region includes a means for creating a projector of the entire degree of freedom display, a means for creating an overlap motion matrix of the entire partial region, and a means for LU decomposing the overlap motion matrix of the entire partial region.

[claim3]
3. The method of claim 1, further comprising:
Wherein the means for performing initial setting of the projection CG method preprocessed for the entire degree of freedom comprises: means for setting an initial displacement of the entire degree of freedom; means for calculating an initial residual of the entire degree of freedom; means for performing diagonal scaling preprocessing calculation; COARSE GRID Means for performing a pre-processing calculation, and means for performing a pre-processing calculation of the total degree of freedom CGAnd means for setting an initial value of a vector of the method search direction.

[claim4]
4. The method of claim 1, further comprising:
Wherein the means for iterative calculation of the projection CG method preprocessed for the entire degree of freedom comprises: means for updating displacement of the entire degree of freedom; means for updating residual difference of the entire degree of freedom; means for performing diagonal scaling preprocessing calculation; COARSE GRID Means for performing preprocessing calculation, means for updating the CG method search direction vector of all degrees of freedom, and means for determining convergence.

[claim5]
5. AMEND STATUS: Delete

[claim6]
6. AMEND STATUS: Delete

[claim7]
7. AMEND STATUS: Delete

[claim8]
8. AMEND STATUS: Delete

[claim9]
9. In a parallel finite element method calculation system that solves a super-large structure problem with a degree of freedom of 1,000,000 or more, a parallel finite element method calculation system is provided that includes means for performing region division, means for distributing partial regions to parts in charge of each processor, means for creating a rigidity matrix, A computer readable recording medium having recorded thereon a parallel finite element method calculation program for causing a computer to function as: means for performing initial setting of a pre-processed projection CG method of an entire degree of freedom; means for performing iterative calculation of the pre-processed projection CG method of the entire degree of freedom; and means for outputting a displacement solution.

[claim10]
10. The method of claim 9, further comprising:
Wherein the means for setting the overlapping motion of the entire partial region functions as a means for creating a projector for displaying the entire degree of freedom, a means for creating an overlapping motion matrix of the entire partial region, and a means for LU decomposing the overlapping motion matrix of the entire partial region.

[claim11]
11. The method of claim 9, further comprising:
Pretreated projection of the overall degree of freedom CGA means for setting an initial displacement of the overall degree of freedom; a means for calculating an initial residual difference of the overall degree of freedom; a means for performing diagonal scaling preprocessing calculation; COARSE GRID The vector initial value of the CG method search direction with respect to the entire degree of freedom; means for performing preprocessing calculation; and means for setting the initial value of the vector in the CG method search direction with respect to the entire degree of freedom.

[claim12]
12. The method of claim 9, further comprising:
Pretreated projection of the overall degree of freedom CGA unit that updates displacement of the entire degree of freedom; a unit that updates residual of the entire degree of freedom; a unit that performs diagonal scaling preprocessing calculation; COARSE GRID A means for performing preprocessing calculation on the vector of the CG method search direction with all degrees of freedom, a means for updating the vector of the CG method search direction with all degrees of freedom, and a means for determining convergence.
  • Applicant
  • ALLIED ENGINEERING
  • JAPAN SCIENCE AND TECHNOLOGY AGENCY
  • Inventor
  • AKIBA HIROSHI
  • OHYAMA TOMONOBU
  • SUZUKI MASABUMI
IPC(International Patent Classification)
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