Visualization	Texture-based contour generation on FEM/BEM higher-order surfaces. A simple and efficient approach to the visualization of FEM/BEM results as color contours is developed. The technique is based on irregular subdivision of higher-order element faces into triangular elements and on using texture interpolation to produce contours. The subdivision density is determined using both face edge curvatures and ranges of result fields over element edges. After determining number of subdivisions along element edges, the face is subdivided into triangles using Delaunay triangulation procedure. Contours of results are generated by texture interpolation. The Java 3D API is used for implementation of the proposed algorithm. Publication: [1], [2]
Nanomechanics	Modeling of self-positioning nanostructures. Self-positioning fabrication procedure is based on the existence of initial strains in lattice-mismatched epitaxial layers. Hinges, tubes and other three-dimensional micro-and nanostructures can be formed by releasing two or more lattice-mismatched epitaxial layers from the substrate. Analytical solutions have been obtained for curvature radius of isotropic and cubic crystal anisotropic self-positioning structures. The finite element method is used for the solution of 3D geometrically nonlinear problems with small strains and large rotations and translation. Effect of size on the self-positioning on nanostructures is investigated with atomic-scale finite element method. Publications: [1], [2], [3]
FEM in Java	Programming finite elements in Java. Using Java for development of finite element programs provides numerous advantages: an object-oriented paradigm, multiplatform support, ease of development, reliability and stability, the ability to use legacy C or C++ code, good documentation, development-tool availability, etc. Java programs are less susceptible to bugs and security flaws. Java provides APIs for development of GUI, and 3D graphics applications. Java is slower than C in performing "multiply-add" arithmetic inside double and triple loops. However, tuning of important Java code fragments provides computational speed comparable to that of C. Book: G.Nikishkov, Programming Finite Elements in Java. Springer, 2010 [Springer] [Amazon]
Augmented reality	An augmented-reality approach to real-time visualization of tactile data with projection on a human organ has been developed. A target procedure is breast cancer examination with a tactile sensor. The special tactile sensor is used to measure tissue stiffness values at discrete points of the examined organ. We developed an augmented reality system which integrates the tactile sensor, a head-mounted display with a small video camera, and a notebook computer. Tracking of the human organ and the tactile sensor is based on optical markers. Results of stiffness measurements are depicted as semi-transparent three-dimensional objects projected on the patient’s body. Different visualization techniques are employed depending on the amount of data and user preference. Publications: [1], [Video]
Adaptive quadtree-octree FEM	Adaptive quadtree-octree finite element algorithm. For quadrilateral and hexahedral finite elements, it is difficult to perform mesh refinement preserving compatibility and element quality. Special refinement elements with some nodes outside element volume are proposed. Elements allow multiple face connection and provide a possibility to refine meshes in quadtree-octree fashion. The following adaptive finite element algorithm is used. Starting with a coarse mesh, element refinement iterations are carried out. At each iteration, the finite element equation system is solved and local element errors are estimated and compared to the specified error tolerance. Elements with excessive errors are divided into four special elements (2D) or eight special elements (3D). Mesh refinement iteration process is terminated when no element splits occur during an iteration. Publication: [1]

G.P.Nikishkov  *  http://www.u-aizu.ac.jp/~niki   *  2010-03-25