This paper presents a novel progressive surface modelling method to construct a freeform surface incrementally based on 3D motion sketches that represent the boundary and interior characteristic curves. The approach can construct a base surface model from multiple boundary curves and support incremental surface updating from interior characteristic curves which may cross the boundary curves or ...

Boundary or interior layer problems of high-dimensional convection–diffusion equations have distinct asymmetry. Consequently, computational grid distributions and linear algebraic systems arising from finite difference schemes for them are also asymmetric. Numerical solutions these kinds more complicated than those symmetric problems. In this paper, we extended our previous work on the partial ...

A spectral method is described for solving coupled elliptic problems on an interior and an exterior domain. The method is formulated and tested on the two-dimensional interior Poisson and exterior Laplace problems, whose solutions and their normal derivatives are required to be continuous across the interface. A complete basis of homogeneous solutions for the interior and exterior regions, corr...

Boundary-layer meshes are important for numerical simulations in computational fluid dynamics, including computational biofluid dynamics of air flow in lungs and blood flow in hearts. Generating boundary-layer meshes is challenging for complex biological geometries. In this paper, we propose a novel technique for generating prismatic boundary-layer meshes for such complex geometries. Our method...

This application paper presents details of the technique we developed to produce an adaptive and quality tetrahedral finite element mesh model of a human heart. Beginning from a polygonal surface model consisting of twenty-two components, we first edit and convert it to volumetric gridded data. A component index for each cell edge and grid point is computed for assisting the boundary and materi...

We consider the problem " 2 u ? u + f (u) = 0 in u > 0 in ; @u @ = 0 on @; (0.1) where is a bounded smooth domain in R N , " > 0 is a small parameter and f is a superlinear, subcritical nonlinearity. It is known that this equation possesses multiple boundary spike solutions that concentrate, as " approaches zero, at multiple critical points of the mean curvature function H(P); P 2 @. It is also...

A grid free method for approximating incompressible boundary layers is introduced. The computational elements are segments of vortex sheets. The method is related to the earlier vortex method; simplicity is achieved at the cost of replacing the Navier-Stokes equations by the Prandtl boundary layer equations. A new method for generating vorticity at boundaries is also presented; it can be used w...

We consider the perturbed elliptic Sine–Gordon ODE with two positive parameters μ and λ, and show the existence of solutions which have 2n multiple interior layers for λ 1. We also determine the location of multiple interior layers as λ→∞.

in this paper, the effect of different boundary conditions on the free vibration analysis response of a sandwich plates is presented using higher order shear deformation theory. the face sheets are orthotropic laminated composite that follow the first order shear deformation theory (fsdt) based on rissners-mindlin (rm) kinematics field. based on energy method and hamilton's principle, the ...

In this paper, an analytical method is developed to obtain the solution for the one dimensional transient thermal and mechanical stresses in a hollow cylinder made of functionally graded material (FGM) and piezoelectric layers. The FGM properties are assumed to depend on the variable r and they are expressed as power functions of r but the Poisson’s ratio is assumed to be constant. Transient te...