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In this paper, we study the preferential stiffness and the crack-tip fields for an elastic porous solid of which material properties are dependent upon the density. Such a description is necessary to describe the failure that can be caused…
We present a continuous finite element method for some examples of fully nonlinear elliptic equation. A key tool is the discretisation proposed in Lakkis & Pryer (2011, SISC) allowing us to work directly on the strong form of a linear PDE.…
This paper is concerned with fully discrete finite element methods for approximating variational solutions of nonlinear stochastic elastic wave equations with multiplicative noise. A detailed analysis of the properties of the weak solution…
A numerical method is proposed for a class of stochastic control problems including singular behavior. This method solves an infinite-dimensional linear program equivalent to the stochastic control problem using a finite element type…
In this paper we revisit random linear under-determined systems with sparse solutions. We consider $\ell_1$ optimization heuristic known to work very well when used to solve these systems. A collection of fundamental results that relate to…
Sim-to-real transfer remains a significant challenge in soft robotics due to the unpredictability introduced by common manufacturing processes such as 3D printing and molding. These processes often result in deviations from simulated…
This paper presents a learnable solver tailored to iteratively solve sparse linear systems from discretized partial differential equations (PDEs). Unlike traditional approaches relying on specialized expertise, our solver streamlines the…
We present a machine-learning strategy for finite element analysis of solid mechanics wherein we replace complex portions of a computational domain with a data-driven surrogate. In the proposed strategy, we decompose a computational domain…
Sparse regression has emerged as a popular technique for learning dynamical systems from temporal data, beginning with the SINDy (Sparse Identification of Nonlinear Dynamics) framework proposed by arXiv:1509.03580. Quantifying the…
Probabilistic solvers for ordinary differential equations (ODEs) provide efficient quantification of numerical uncertainty associated with simulation of dynamical systems. Their convergence rates have been established by a growing body of…
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…
In this paper, we present a construction of a `matching sparsifier', that is, a sparse subgraph of the given graph that preserves large matchings approximately and is robust to modifications of the graph. We use this matching sparsifier to…
Driven by the challenging task of finding robust discretization methods for Galbrun's equation, we investigate conditions for stability and different aspects of robustness for different finite element schemes on a simplified version of the…
This work develops a convergence theory for H(div)-conforming finite element methods applied to the steady Oseen problem, focusing on cases where the exact finite element complex holds while the commuting diagram property may fail. The…
Graph sketching has emerged as a powerful technique for processing massive graphs that change over time (i.e., are presented as a dynamic stream of edge updates) over the past few years, starting with the work of Ahn, Guha and McGregor…
Applications in quantitative finance such as optimal trade execution, risk management of options, and optimal asset allocation involve the solution of high dimensional and nonlinear Partial Differential Equations (PDEs). The connection…
This article aims to demonstrate and discuss the applications of automatic differentiation (AD) for finding derivatives in PDE-constrained optimization problems and Jacobians in non-linear finite element analysis. The main idea is to…
Motivated by problems where the response is needed at select localized regions in a large computational domain, we devise a novel finite element discretization that results in exponential convergence at pre-selected points. The two key…
In this work, we present an effective discrete Edwards-Wilkinson equation aimed to describe the single-file diffusion process. The key physical properties of the system are captured defining an effective elasticity, which is proportional to…
We propose an effective and flexible way to implement 2D and 3D elastoplastic problems in MATLAB using fully vectorized codes. Our technique is applied to a broad class of the problems including perfect plasticity or plasticity with…