Weakly Singular Symmetric Galerkin Boundary Element Method for Fracture Analysis of Three-Dimensional Structures Considering Rotational Inertia and Gravitational Forces

The Symmetric Galerkin Boundary Element Method is advantageous for the linear elastic fracture and crackgrowth analysis of solid structures,because only boundary and crack-surface elements are needed.However,for engineering structures subjected to body forces such as rotational inertia and gravitational loads,additional domain integral terms in the Galerkin boundary integral equation will necessitate meshing of the interior of the domain.In this study,weakly-singular SGBEM for fracture analysis of three-dimensional structures considering rotational inertia and gravitational forces are developed.By using divergence theorem or alternatively the radial integration method,the domain integral terms caused by body forces are transformed into boundary integrals.And due to the weak singularity of the formulated boundary integral equations,a simple Gauss-Legendre quadrature with a few integral points is sufficient for numerically evaluating the SGBEM equations.Some numerical examples are presented to verify this approach and results are compared with benchmark solutions.

The Existence of Harmonic Maps from an Annulus to S^2 with Symmetric Boundary Value

In this paper, we use the deformation method andG-equivariant theory to prove the existence and multiplicity of harmonic maps from an annulus to the unit sphere in? 3 with symmetric boundary value. In particular, we can get infinitely many homotopically different harmonic maps if the boundary value isS 1-equivariant and nonconstant.

A truncated implicit high-order finite-difference scheme combined with boundary conditions

In this paper, first we calculate finite-difference coefficients of implicit finite- difference methods （IFDM） for the first and second-order derivatives on normal grids and first- order derivatives on staggered grids and find that small coefficients of high-order IFDMs exist. Dispersion analysis demonstrates that omitting these small coefficients can retain approximately the same order accuracy but greatly reduce computational costs. Then, we introduce a mirrorimage symmetric boundary condition to improve IFDMs accuracy and stability and adopt the hybrid absorbing boundary condition （ABC） to reduce unwanted reflections from the model boundary. Last, we give elastic wave modeling examples for homogeneous and heterogeneous models to demonstrate the advantages of the proposed scheme.

Feasibility study of symmetric solution of molecular argon flow inside microscale nozzles

The computational cost of numerical methods in microscopic-scales such as molecular dynamics(MD) is a deterrent factor that limits simulations with a large number of particles. Hence, it is desirable to decrease the computational cost and run time of simulations, especially for problems with a symmetrical domain. However, in microscopic-scales, implementation of symmetric boundary conditions is not straightforward. Previously, the present authors have successfully used a symmetry boundary condition to solve molecular flows in constant-area channels. The results obtained with this approach agree well with the benchmark cases. Therefore, it has provided us with a sound ground to further explore feasibility of applying symmetric solutions of micro-fluid flows in other geometries such as variable-area ducts. Molecular flows are solved for the whole domain with and without the symmetric boundary condition. Good agreement has been reached between the results of the symmetric solution and the whole domain solution. To investigate robustness of the proposed method, simulations are conducted for different values of affecting parameters including an external force, a flow density, and a domain length. The results indicate that the symmetric solution is also applicable to variable-area ducts such as micro-nozzles.

THE SYMMETRIC POSITIVE SOLUTIONS OF 2n-ORDER BOUNDARY VALUE PROBLEMS ON TIME SCALES

In this paper, we are concerned with the symmetric positive solutions of a 2n-order boundary value problems on time scales. By using induction principle,the symmetric form of the Green＇s function is established. In order to construct a necessary and sufficient condition for the existence result, the method of iterative technique will be used. As an application, an example is given to illustrate our main result.

Area-preserving mean curvature flow of rotationally symmetric hypersurfaces with free boundaries

We consider the area-preserving mean curvature flow with free Neumann boundaries. We show that a rotationally symmetric n-dimensional hypersurface in R^(n+1)between two parallel hyperplanes will converge to a cylinder with the same area under this flow. We use the geometric properties and the maximal principle to obtain gradient and curvature estimates, leading to long-time existence of the flow and convergence to a constant mean curvature surface.

Optimal L_∞ Estimates for Galerkin Methods for Nonlinear Singular Two-point Boundary Value Problems

In this paper, we apply the symmetric Galerkin methods to the numerical solutions of a kind of singular linear two-point boundary value problems. We estimate the error in the maximum norm. For the sake of obtaining full superconvergence uniformly at all nodal points, we introduce local mesh refinements. Then we extend these results to a class of nonlinear problems. Finally, we present some numerical results which confirm our theoretical conclusions.

VISCOSITY SOLUTION THEORY OF A CLASS OF NONLINEAR DEGENERATE PARABOLIC EQUATIONS Ⅱ. LIPSCHITZ CONTINUITY OF FREE BOUNDARY

In [1] we construct a unique bounded H■lder continuous viscosity solution for the nonlinear PDEs with the evolution p-Laplacian equation and its anisotropic version as typical examples. In this part, we investigate the Lipschitz continuity of the free boundary of viscosity solution and its asymptotic spherical symmetricity, however,this result does not include the anisotropic case.