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Abstract: A finite difference method (FDM) for multi-dimensional nonlinear coupled system of parabolic and hyperbolic equations is studied. Nonlinear coupled property is fully considered. Variant techniques of discrete functional analysis such as summation by parts and deductive reasoning are used to make prior estimates. The FD scheme is uniquely solvable and unconditionally stable. With the approximation property of the scheme, the convergence is obtained with a rate of order. [Copyright &y& Elsevier]

Abstract: An unstructured tetrahedral mesh generation algorithm for 3D model with constraints is presented. To automatically generate a tetrahedral mesh for model with constraints, an advancing front algorithm is presented based on conforming constrained Delaunay tetrahedralization (CCDT). To reduce the number of visibility tests between vertices with respect to model faces as well as the computation of constrained Delaunay tetrahedra, a sufficient condition for DT (constrained Delaunay tetrahedralization whose simplexes are all Delaunay) existence is presented and utilized coupled to uniform grid and advancing front techniques in our algorithm. The mesh generator is robust and exhibits a linear time complexity for mechanical models with uniform density distribution. [Copyright &y& Elsevier]

Abstract: This paper proposes a second order geometric iteration algorithm for point projection and inversion on parametric surfaces. The iteration starts from an initial projection estimation. In each iteration, we construct a second order osculating torus patch to the parametric surface at the previous projection. Then we project the test point onto the torus patch to compute the next projection and its parameter. This iterative process is terminated when the parameter satisfies the required precision. Experiments demonstrate the convergence speed of our algorithm. [Copyright &y& Elsevier]

Abstract: Dynamic partial differential equation (PDE) parametric curves which can be expressed as a coupled system of two hyperbolic equations are developed. In curve design, dynamic PDE parametric curves can be modified intuitively and are more flexible than ordinary differential equation (ODE) curves. The calculation of dynamic PDE parametric curves must recur to numerical methods and a three-level finite difference scheme is proposed. Approximation and stability properties for the scheme are proved and convergence property is derived. An example of interpolating PDE curves is presented as an application of dynamic PDE parametric curves. [Copyright &y& Elsevier]

Abstract: A novel and efficient quasi-Monte Carlo method for computing the area of a point-sampled surface with associated surface normal for each point is presented. Our method operates directly on the point cloud without any surface reconstruction procedure. Using the Cauchy–Crofton formula, the area of the point-sampled surface is calculated by counting the number of intersection points between the point cloud and a set of uniformly distributed lines generated with low-discrepancy sequences. Based on a clustering technique, we also propose an effective algorithm for computing the intersection points of a line with the point-sampled surface. By testing on a number of point-based models, experiments suggest that our method is more robust and more efficient than those conventional approaches based on surface reconstruction. [Copyright &y& Elsevier]