Related papers: Coupled variational formulations of linear elastic…
This paper presents a new and unified approach to the derivation and analysis of many existing, as well as new discontinuous Galerkin methods for linear elasticity problems. The analysis is based on a unified discrete formulation for the…
In this paper, we propose and study neural network based methods for solutions of high-dimensional quadratic porous medium equation (QPME). Three variational formulations of this nonlinear PDE are presented: a strong formulation and two…
Vertical decomposition is a widely used general technique for decomposing the cells of arrangements of semi-algebraic sets in ${{\mathbb R}}^d$ into constant-complexity subcells. In this paper, we settle in the affirmative a few…
This paper proposes a domain decomposition subspace neural network method for efficiently solving linear and nonlinear partial differential equations. By combining the principles of domain decomposition and subspace neural networks, the…
The discovery of partial differential equations (PDEs) is a challenging task that involves both theoretical and empirical methods. Machine learning approaches have been developed and used to solve this problem; however, it is important to…
This work presents a multiscale model reduction approach to discontinuous fields identification problems in the framework of Bayesian inference. An ensemble-based variable separation (VS) method is proposed to approximate multiscale basis…
Solving the linear elasticity and Stokes equations by an optimal domain decomposition method derived algebraically involves the use of non standard interface conditions. The one-level domain decomposition preconditioners are based on the…
A technique for developing convex dual variational principles for the governing PDE of nonlinear elastostatics and elastodynamics is presented. This allows the definition of notions of a variational dual solution and a dual solution…
In this paper, a new computational framework based on the topology derivative concept is presented for evaluating stochastic topological sensitivities of complex systems. The proposed framework, designed for dealing with high dimensional…
While crack nucleation and propagation in the brittle or quasi-brittle regime can be predicted via variational or material-force-based phase field fracture models, these models often assume that the underlying elastic response of the…
A system of partial differential equations (PDEs) is derived to compute the full-field stress from an observed kinematic field when the flow rule governing the plastic deformation is unknown. These equations generalize previously proposed…
We overview a series of recent works addressing numerical simulations of partial differential equations in the presence of some elements of randomness. The specific equations manipulated are linear elliptic, and arise in the context of…
This paper deals with the solution of large classes of systems of nonlinear partial differential equations (PDEs) in spaces of generalized functions that are constructed as the completion of uniform convergence spaces. The existence result…
We consider the problem of solving partial differential equations (PDEs) in domains with complex microparticle geometry that is impractical, or intractable, to model explicitly. Drawing inspiration from volume rendering, we propose tackling…
We present an iterative scheme, reminiscent of the Multigrid method, to solve large boundary value problems with Probabilistic Domain Decomposition (PDD). In it, increasingly accurate approximations to the solution are used as control…
The Discrete Dislocation (DD) analysis and its computional modeling have been advanced significantly over the past decade. This progress has been further magnified by the idea to couple DD with continuum mechanics analysis in association…
We present a finite element discretisation to model the interaction between a poroelastic structure and an elastic medium. The consolidation problem considers fully coupled deformations across an interface, ensuring continuity of…
We develop a linear-algebraic framework for dimensional analysis in systems with constraints, particularly when variables are numerous or related by implicit relations so that direct elimination is impractical. By expressing both…
We extend a phase-field/gradient damage formulation for cohesive fracture to the dynamic case. The model is characterized by a regularized fracture energy that is linear in the damage field, as well as non-polynomial degradation functions.…
The recent development of spectral method has been praised for its high-order convergence in simulating complex physical problems. The combination of embedded boundary method and spectral method becomes a mainstream way to tackle…