This study focuses on the optimization of the plane structure. Sequential quadratic programming (SQP) will be utilized, which is one of the most efficient methods for solving nonlinearly constrained optimization problems. A new formulation for the second order sensitivity analysis of the two-dimensional finite element will be developed. All the second order required derivatives will be calculat...

In this paper, symmetric water entry of twin wedges is investigated for deadrise angle of 30 degree. Three numerical simulation of a symmetric impact, considering rigid body dynamic equations of motion in two-phase flow is presented. The two-phase flow around the wedges is solved by Finite Element based on Finite Volume method (FEM-FVM) which is used in conjunction with Volume of Fluid (VOF) sc...

In this work, we present a novel method to approximate stiff problems using a finite volume (FV) discretization. The stiffness is caused by the existence of a small parameter in the equation which introduces a boundary layer. The semi-analytic method consists in adding in the finite volume space the boundary layer corrector which encompasses the singularities of the problem. We verify the stabi...

An extended finite element method (XFEM) for the forward model of 3D optical molecular imaging is developed with simplified spherical harmonics approximation (SP(N)). In XFEM scheme of SP(N) equations, the signed distance function is employed to accurately represent the internal tissue boundary, and then it is used to construct the enriched basis function of the finite element scheme. Therefore...

A new variational (dis)continuous Galerkin finite element method is presented for linear free surface gravity water wave equations. In this method, the space-time finite element discretization is based on a discrete variational formulation analogous to a version of Luke’s variational principle. The finite element discretization results into a linear algebraic system of equations with a symmetri...

We present a new mixed finite element method for solving the extended Fisher-Kolmogorov (EFK) equation. We first decompose the EFK equation as the two second-order equations, then deal with a second-order equation employing finite element method, and handle the other second-order equation using a new mixed finite element method. In the new mixed finite element method, the gradient ∇u belongs to...

We prove the convergence of a semi-implicit monotone finite difference scheme approximating an initial-boundary value problem for a spatially one-dimensional quasilinear strongly degenerate parabolic equation, which is supplied with two different inhomogeneous flux-type boundary conditions. This problem arises in the modeling of the sedimentation-consolidation process. We formulate the definiti...