This research aims at establishment of integrated analysis methods for general continua.
As the first step toward the goal, principles of solid (Lagrangean) mechanics are described in a unified form.
The theory is then implemented to a simple and general simulation algorithm with high efficiency as well as amenability to parallel processing.
For applying the methodology to more complex systems, several related techniques have also been developed.
(i) simple surface interpolation (Nagata patch), allowing geometric representation with high precision;
(ii) optimized integration on arbitrary multidimensional domains, enabling accurate evaluation of physical quantities;
(iii) numerical solution of multivariate polynomial systems, which appear in subproblems.
The above mathematical tools are useful also in many other areas of computational science and engineering
「Interpolation of Multidimensional Scattered Data Based on Error Bound」
VCAD System Research 2009, May 2010, pp. 73-85. (in Japanese).
「Smooth Local Interpolation of Surfaces Using Normal Vectors
Journal of Applied Mathematics, Vol. 2010, 2010, pp. 1-24, Article ID 952420, doi:10.1155/2010/952420,
「Simple Local Interpolation of Surfaces Using Normal Vectors」
Computer Aided Geometric Design, Vol. 22, No. 4, May 2005, pp.327-347.
「Numerical Solution Algorithm for Multivariate Polynomial Systems」
The 5th Symposium on Integrated Volume-CAD System Research, June 2005, pp. 20-39 (in Japanese)
「Variable-Gain Constraint Stabilization for General Multibody Systems with Applications'
Journal of Vibration and Control, Vol. 10, 2004, pp. 1335-1357.
「Analysis of 3-D Mechanics Using an Arbitrarily-Shaped Element with Associated Techniques」
Journal of the Japan Society for Simulation Technology,Vol. 23, No. 4, December 2004, pp. 272-278. (in Japanese).
「New Techniques for 3-D Mechanical Analysis」
The 4th Symposium on Integrated Volume-CAD System Research, July 2004, pp. 75-86 (in Japanese).