相关论文: Mixed variational formulations for structural topo…
In this work, we consider fracture propagation in nearly incompressible and (fully) incompressible materials using a phase-field formulation. We use a mixed form of the elasticity equation to overcome volume locking effects and develop a…
This paper outlines a rigorous variational-based multilevel Global-Local formulation for ductile fracture. Here, a phase-field formulation is used to resolve failure mechanisms by regularizing the sharp crack topology on the local state.…
We introduce a new abstraction for the representation and solution of multi-domain problems using finite element methods. This is an advance over previous work in that it achieves a single higher-level abstraction that represents…
The governing equations of the variational approach to brittle and ductile fracture emerge from the minimization of a non-convex energy functional subject to irreversibility constraints. This results in a multifield problem governed by a…
This paper is concerned with topology optimization based on a level set method using (doubly) nonlinear diffusion equations. Topology optimization using the level set method is called level set-based topology optimization, which is possible…
In this paper, we develop an online basis enrichment method with the mortar mixed finite element method, using the oversampling technique, to solve for flow problems in highly heterogeneous media. We first compute a coarse grid solution…
Uniform flow distribution across parallel channels directly impacts the performance and efficiency of many fluid and energy systems. However, designing efficient flow manifolds that ensure uniform flow distribution remains a challenge. This…
We consider implementational aspects of the mixed finite element method for a special class of nonlinear problems. We establish the equivalence of the hybridized formulation of the mixed finite element method to a nonconforming finite…
The classical dynamic programming-based optimal stochastic control methods fail to cope with nonseparable dynamic optimization problems as the principle of optimality no longer applies in such situations. Among these notorious nonseparable…
We propose a novel optimization framework for computing the medial axis transform that simultaneously preserves the medial structure and ensures high medial mesh quality. The medial structure, consisting of interconnected sheets, seams, and…
We develop a high order reconstructed discontinuous approximation (RDA) method for solving a mixed formulation of the quad-curl problem in two and three dimensions. This mixed formulation is established by adding an auxiliary variable to…
We study optimal design problems involving variational inequalities with unilateral conditions in the domain and pointwise boundary observation. We use regularizing and penalization tehniques in the setting of the Hamiltonian approach to…
We show how two-dimensional mixed finite element methods that satisfy the conditions of finite element exterior calculus can be used for the horizontal discretisation of dynamical cores for numerical weather prediction on pseudo-uniform…
We introduce a novel hybrid algorithm to simulate the real-time evolution of quantum systems using parameterized quantum circuits. The method, named "projected - Variational Quantum Dynamics" (p-VQD) realizes an iterative, global projection…
It is well known over the recent years that measuring the success of projects under the umbrella of project management is inextricably linked with the associated cost, time, and quality. Most of the previous researches in the field assigned…
We develop a space-time mortar mixed finite element method for parabolic problems. The domain is decomposed into a union of subdomains discretized with non-matching spatial grids and asynchronous time steps. The method is based on a…
In this work, we consider unfitted finite element methods for the numerical approximation of the Stokes problem. It is well-known that this kind of methods lead to arbitrarily ill-conditioned systems. In order to solve this issue, we…
In this paper, we present a novel framework for deriving the evolution equation of the level set function in topology optimization, departing from conventional Hamilton-Jacobi based formulations. The key idea is the introduction of an…
We consider mechanics of composite materials in which thin inclusions are modeled by lower-dimensional manifolds. By successively applying the dimensional reduction to junctions and intersections within the material, a geometry of…
In this paper we devise and analyze a mixed finite element method for a modified Cahn-Hilliard equation coupled with a non-steady Darcy-Stokes flow that models phase separation and coupled fluid flow in immiscible binary fluids and diblock…