Refereed Publications

1. M. Savchenko, O. Egorova, I. Hagiwara, V. Savchenko, “Techniques for Improving the Quality of Tetrahedral Meshes”, Transaction of Society of Automotive Engineers of Japan (JSAE), vol.38, No.2, March, 2007, pp. 299-306.
   Abstract - Mesh improvement is an almost obligatory step for obtaining a valid finite element because the requirements of an automatic mesh generator can be weakened. In this paper we suggest a method based on an implementation of quasi-statistical modeling, which can produce elements with a Gaussian (normal) distribution and a method based on decomposition of the local tetrahedral elements domain into a bundle of the plane elements. A main approach used in these local improvement methods is finally based on averaging the coordinates of all the nodes of the neighbour elements as is done in Laplacian smoothing technique. We also suggest a new method for tetrahedral mesh improvement based on the use of space mapping technique based on radial basis functions instead of using mesh smoothing technique based on averaging the coordinates. We demonstrate that our techniques can be applied to 3D volume meshes. Experimental results are included to demonstrate the functionality of our methods.
2. O. Egorova, M. Savchenko, I. Hagiwara, and V. Savchenko, “Modeling of Quality Parameter Values for Improving Meshes”, Japan Journal of Industrial and Applied Mathematics (JJIAM), vol. 24 (2007), pp. 181-195.
   Abstract - A novel quasi-statistical approach to improve the quality of triangular surface meshes is presented. The present method is based on modeling of an event of mesh improvement. This event is modeled via modeling of a discrete random variable. The random variable is modeled in a tangent plane of each local domain of the mesh. One domain collects several elements with a common point. Values of random variable are calculated by modeling formula according to the initial sampling data of the projected elements with respect to all neighbors of the domain. Geometrical equivalent called a potential form is constructed for each element of the domain with a mesh quality parameter value equal to the modeled numerical value. Such potential forms create potential centers of the domain. Averaging the coordinates of potential centers of the domain gives a new central point position. After geometrical realization over entire mesh, the shapes of triangular elements are changed according to the normal distribution. It is shown experimentally that the mean of the final mesh is better than the initial one in most cases, so the event of the mesh improvement is likely occurred. Moreover, projection onto a local tangent plane included in the algorithm allows preservation of the model volume enclose by the surface mesh. The implementation results are presented to demonstrate the functionality of the method. Our approach can provide a flexible tool for the development of mesh improvement algorithms, creating better-input parameters for the triangular meshes and other kind of meshes intended to be applied in finite element analysis or computer graphics.
3. V. Savchenko, M. Savchenko, O. Egorova, I. Hagiwara, “Mesh Quality Improvement: Radial Basis Functions Approach”, Journal of Algorithms and Computational Technology (JACT), vol. 2(3), ISNN 1748-3018, Multi-Science Publishing Company, 2007 (accepted).
   Abstract - In this paper, we present a novel method, based on an implementation of space mapping technique, for improvement of the quality of tetrahedral and hexahedral meshes. The same approach is used for surface meshes where geometry of the initial surface mesh is preserved by a local mesh improvement such that new positions of the interior nodes of the mesh remain on the original discrete surface. The proposed method can be used in a pre-processing stage for subsequent studies (finite element analysis, computer graphics, etc.) by providing better input parameters for these processes. Experimental results are included to demonstrate the functionality of our method.
4. V. Savchenko, M. Savchenko, O. Egorova, I. Hagiwara, “The Shannon Entropy-based Node Placement for Enrichment and Simplification of Meshes”, In Proceedings of ICCS 2007 International Conference. 7-th International Conference on Computational Science, Lecture Notes in Computer Science, LNCS 4488, Springer-Verlag, vol2, pp. 65-72 , 2007.
   Abstract - In this paper, we present a novel simple method based on the idea of exploiting the Shannon entropy as a measure of the inter-influence relationships between neighboring nodes of a mesh to optimize node locations. The method can be used in a pre-processing stage for subsequent studies such as finite element analysis by providing better input parameters for these processes. Experimental results are included to demonstrate the functionality of our method.
5. M. Sugihara and V. Savchenko, “A Combination of Hierarchical Structures and Particle Systems for Self-Collision Detection of Deforming Objects”, Proceedings GRAPHICON’2007, 2007.
   Abstract - The paper proposes an approach which combines hierarchical structures and particle systems for self-collision detection occurring in a deformable object. Numerous algorithms for collision detection have been proposed in computer graphics applications. Our algorithm exploits the efficiency of hierarchical structures to deal with many polygons, and particle systems because they can be used to extract colliding polygons. We have extended these two algorithms to deal with self-collision detection. The approach is split into two stages. Particles are distributed on the surface of a deformable object. Then, if the particles detect a possibility of a selfcollision, hierarchical self-collision detection is started. The algorithm has been implemented on a square cloth model as an example of a deformable object. We show that the algorithm efficiently reduces self-collision detection redundancy, and yet precisely detects self-collision events we present a novel simple method based on the idea of exploiting the Shannon entropy as a measure of the inter-influence relationships between neighboring nodes of a mesh to optimize node locations. The method can be used in a pre-processing stage for subsequent studies such as finite element analysis by providing better input parameters for these processes. Experimental results are included to demonstrate the functionality of our method.

Other Publications

1. M. Savchenko, V. Savchenko, O. Egorova, I. Hagiwara, “Applying the Shannon entropy to Mesh Processing: Quality Improvement”, In Proceedings of the JSIAM 2007 Annual Congress, Hokkaido, Japan pp.148-149, 2007.
2. O. Egorova, M. Savchenko, V. Savchenko, I. Hagiwara, “Hexahedral growth model: new guide for hexahedral meshing”, In Proceedings 23-06 of the JSIAM 2007 Annual Congress, Hokkaido, Japan pp.154-155, 2007.
3. M. Savchenko, O. Egorova, I. Hagiwara, V. Savchenko, Tetrahedral Mesh Reduction Technique. APCOM’07 in conjunction with EPMESC XI, December 3-6, 2007, Kyoto, JAPAN, CD Proceedings.
4. O. Egorova, M. Savchenko, V. Savchenko, I. Hagiwara, Topology and Geometry of Hexahedral Complex: Combined Approach for Hexahedral Meshing, APCOM’07 symposium in conjunction with EPMESC XI, December 3-6, 2007, Kyoto, JAPAN, CD Proceedings.

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