TIME DISCONTINUOUS GALERKIN FINITE ELEMENT METHOD FOR DYNAMIC ANALYSES IN SATURATED PORO-ELASTO-PLASTIC MEDIUM

A time-discontinuous Galerkin finite element method for dynamic analyses in saturated poro-elasto-plastic medium is proposed.As compared with the existing discontinuous Galerkin finite element methods,the distinct feature of the proposed method is that the continuity of the displacement vector at each discrete time instant is automatically ensured,whereas the discontinuity of the velocity vector at the discrete time levels still remains.The computational cost is then obviously reduced, particularly,for material non-linear problems.Both the implicit and explicit algorithms to solve the derived formulations for material non-linear problems are developed.Numerical results show a good performance of the present method in eliminating spurious numerical oscillations and providing with much more accurate solutions over the traditional Galerkin finite element method using the Newmark algorithm in the time domain.

Time discontinuous Galerkin space-time finite element method for nonlinear Sobolev equations

This article presents a complete discretization of a nonlinear Sobolev equation using space-time discontinuous Galerkin method that is discontinuous in time and continuous in space. The scheme is formulated by introducing the equivalent integral equation of the primal equation. The proposed scheme does not explicitly include the jump terms in time, which represent the discontinuity characteristics of approximate solution. And then the complexity of the theoretical analysis is reduced. The existence and uniqueness of the approximate solution and the stability of the scheme are proved. The optimalorder error estimates in L2 （H1） and L2 （L2） norms are derived. These estimates are valid under weak restrictions on the space-time mesh, namely, without the condition kn ≥ ch2, which is necessary in traditional space-time discontinuous Galerkin methods. Numerical experiments are presented to verify the theoretical results.

DISCONTINUOUS GALERKIN TIME DOMAIN METHOD FOR SOI THIN-RIDGE WAVEGUIDE PROBLEM

A novel high-order three-dimensional(3-D)discontinuous Galerkin time domain(DGTD)method based on a normalized formulation of Maxwell′s equations is developed for modeling and simulating silicon-on-insulator(SOI)thin-ridge waveguide.The DGTD method employs unstructured meshes and piecewise high-order polynomials for spatial discretization,and Runge-Kutta methods for time integration.It is found that the numerical results of the leakage loss of SOI thin-ridge waveguide agree well with those of analytical solutions,which proves that the proposed method is an ideal tool for the quantitative analysis for SOI thin-ridge waveguide.

A comparative study of using two numerical strategies to simulate the biochemical processes in microbially induced calcite precipitation

In this study,we carried out a comparative study of two different numerical strategies for the modeling of the biogeochemical processes in microbially induced calcite precipitation(MICP)process.A simplified MICP model was used,which is based on the mass transport theory.Two numerical strategies,namely the operator splitting(OS)and the global implicit(GI)strategies,were adopted to solve the coupled reactive mass transport problems.These two strategies were compared in the aspects of numerical accuracy,convergence property and computational efficiency by solving the presented MICP model.To look more into the details of the model,sensitivity analysis of some important modeling parameters was also carried out in this paper.