相关论文: A C0 Interior Penalty Method for the Phase Field C…
This paper is devoted to the analysis of a numerical scheme based on the Finite Element Method for approximating the solution of Koiter's model for a linearly elastic elliptic membrane shell subjected to remaining confined in a prescribed…
Central quantities in spectroscopy and magnetism of transition ions in crystals are crystal field parameters (CFPs). Nature self-imposed limits on orthorhombic and lower symmetry CFPs, and existence of intrinsically incomparable CFP sets…
We present a stabilized finite element method for the numerical solution of cavitation in lubrication, modeled as an inequality-constrained Reynolds equation. The cavitation model is written as a variable coefficient saddle-point problem…
We present a short step interior point method for solving a class of nonlinear programming problems with quadratic objective function. Convex quadratic programming problems can be reformulated as problems in this class. The method is shown…
We propose a numerical method to solve general hyperbolic systems in any space dimension using forward Euler time stepping and continuous finite elements on non-uniform grids. The properties of the method are based on the introduction of an…
A finite element method is presented to compute time harmonic microwave fields in three dimensional configurations. Nodal-based finite elements have been coupled with an absorbing boundary condition to solve open boundary problems. This…
We develop a finite element method for the vector Laplacian based on the covariant derivative of tangential vector fields on surfaces embedded in $\mathbb{R}^3$. Closely related operators arise in models of flow on surfaces as well as…
Self-consistent field theory (SCFT) has proven to be a powerful tool for modeling equilibrium microstructures of soft materials, particularly for multiblock polymers. A very successful approach to numerically solving the SCFT set of…
We modify the well-known interior penalty finite element discretization method so that it allows for element-by-element assembly. This is possible due to the introduction of additional unknowns associated with the interfaces between…
In this paper, we study an infeasible interior-point method for linear optimization with full-Newton step. The introduced method uses an algebraic equivalent transformation on the centering equation of the system which defines the central…
This paper discusses lowest-order nonstandard finite element methods for space discretization and explicit and implicit schemes for time discretization of the biharmonic wave equation with clamped boundary conditions. A modified Ritz…
The standard approach to encoding constraints in quantum optimization is the quadratic penalty method. Quadratic penalties introduce additional couplings and energy scales, which can be detrimental to the performance of a quantum optimizer.…
We present a high order, Fourier penalty method for the Maxwell's equations in the vicinity of perfect electric conductor boundary conditions. The approach relies on extending the smooth non-periodic domain of the equations to a periodic…
Explicit time-marching schemes are popular for solving time-dependent partial differential equations; one of the biggest challenges these methods suffer is increasing the critical time-marching step size that guarantees numerical stability.…
We propose an implicit iterative algorithm for an exact penalty method arising from inequality constrained optimization problems. A rapidly convergent fixed point method is developed for a regularized penalty functional. The applicability…
This work develops and analyzes a variational-monolithic unfitted finite element formulation of a linear fluid-structure interaction problem in Eulerian coordinates with a fixed interface. The overall discretization is based on a backward…
This paper studies the problem of stability of a parameterized delay differential equations (DDE see equation (0.1)). After discretizing the DDE (0.1), we show that the problem can be equivalently casted into a semi-definite programming…
We consider fully discrete schemes based on the scalar auxiliary variable (SAV) approach and stabilized SAV approach in time and the Fourier-spectral method in space for the phase field crystal (PFC) equation. Unconditionally energy…
Finite difference method and pseudo-spectral method have been widely used in the numerical relativity to solve the Einstein equations. As the third major category method to solve partial differential equations, finite element method is much…
An integro-differential equation of hyperbolic type, with mixed boundary conditions, is considered. A continuous space-time finite element method of degree one is formulated. A posteriori error representations based on space-time cells is…