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# Orthogonal basis bubble function element numerical analysis method, orthogonal basis bubble function element numerical analysis program, and orthogonal basis bubble function element numerical analyzing apparatus

Foreign code F110005493 K07604WO Sep 6, 2011 United States of America 79165905 20070299641 7881912 Nov 25, 2005 Dec 27, 2007 Feb 1, 2011 JP2005021727 WO2006057359 Nov 25, 2005 Jun 1, 2006 P2004-343213 (Nov 26, 2004) JP P2005-071239 (Mar 14, 2005) JP 2005WO-JP21727 (Nov 25, 2005) WO Orthogonal basis bubble function element numerical analysis method, orthogonal basis bubble function element numerical analysis program, and orthogonal basis bubble function element numerical analyzing apparatus (US7881912)A known analytical physical quantity of an analysis subject and an element level consistent mass matrix of each element are obtained by acquiring units. A bubble function is integrated for each element, and the element level diagonal mass matrix of each element is computed by substituting the value that is integrated for the element level consistent mass matrix of each element. The diagonal mass matrix for the entire analysis region is computed by the summation (superposition) of the element level diagonal mass matrices of each element and inverse matrix thereof is computed. A motion of the analysis subject is analyzed based on the known analytical physical quantity, the diagonal mass matrix for the entire analysis region, and the inverse matrix thereof. [claim1]1. A numerical analysis method, comprising: acquiring a consistent mass matrix of each element of a subject; generating, based on a bubble function of each element, a first diagonal mass matrix of each element, the first diagonal mass matrix being the consistent mass matrix that is diagonalized; analyzing a motion of the subject based on a known physical quantity of the subject and the first diagonal mass matrix; and computing a second diagonal mass matrix of an entire analysis region based on the first diagonal mass matrix, wherein the generating includes generating the first diagonal mass matrix by substituting an integration value of the bubble function of each element into the consistent mass matrix, wherein the integration value is found by employing the following equations: (Equation image 90 not included in text)[claim2]2. A numerical analysis method, comprising: acquiring a consistent mass matrix of each element of a subject; generating, based on a bubble function of each element, a first diagonal mass matrix of each element, the first diagonal mass matrix being the consistent mass matrix that is diagonalized; and analyzing a motion of the subject based on a known physical quantity of the subject and the first diagonal mass matrix, further comprising: computing a second diagonal mass matrix of an entire analysis region based on the first diagonal mass matrix; and computing an inverse matrix of the second diagonal mass matrix, wherein the analyzing includes analyzing the motion based on the known physical quantity, the second diagonal mass matrix, and the inverse matrix, wherein the generating includes generating the first diagonal mass matrix by substituting an integration value of the bubble function of each element into the consistent mass matrix, wherein the integration value is found by employing the following equations: (Equation image 91 not included in text)[claim3]3. A numerical analysis apparatus, comprising: an acquiring unit that acquires a consistent mass matrix of each element of a subject; a generating unit that, based on a bubble function of each element, generates a first diagonal mass matrix of each element, the first diagonal mass matrix being the consistent mass matrix that is diagonalized; and an analyzing unit that analyzes a motion of the subject based on a known physical quantity of the subject and the first diagonal mass matrix, further comprising: a first computing unit that computes a second diagonal mass matrix of the entire subject based on the first diagonal mass matrix; and a second computing unit that computes an inverse matrix of the second diagonal mass matrix, wherein the analyzing unit analyzes the motion based on the known physical quantity, the second diagonal mass matrix, and the inverse matrix, wherein the generating includes generating the first diagonal mass matrix by substituting an integration value of the bubble function of each element into the consistent mass matrix, wherein the integration value is found by employing the following equations: (Equation image 92 not included in text) MATSUMOTO JUNICHI JAPAN SCIENCE AND TECHNOLOGY AGENCY NATIONAL INSTITUTE OF ADVANCED INDUSTRIAL SCIENCE AND TECHNOLOGY G06F  17/10      Complex mathematical operations G06F  17/50      Computer-aided design PRESTO The Innovation of Simulation Technology and the Construction of Foundations for its Practical Use AREA      