Related papers: Deflation-based preconditioning for immersed finit…

Preconditioning has long been a staple technique in optimization, often applied to reduce the condition number of a matrix and speed up the convergence of algorithms. Although there are many popular preconditioning techniques in practice,…

We develop a new optimisation technique that combines multiresolution subdivision surfaces for boundary description with immersed finite elements for the discretisation of the primal and adjoint problems of optimisation. Similar to wavelets…

In this paper, we address the efficient numerical solution of linear and quadratic programming problems, often of large scale. With this aim, we devise an infeasible interior point method, blended with the proximal method of multipliers,…

We derive a mixture theory-based mathematical model of the degradation of a poroelastic solid immersed in a fluid bath. The evolution of the solid's mechanical and transport properties are also modeled. The inspiration for the model is the…

A class of preconditioners is introduced to enhance geometry optimisation and transition state search of molecular systems. We start from the Hessian of molecular mechanical terms, decompose it and retain only its positive definite part to…

The geometric iterative method (GIM) is widely used in data interpolation/fitting, but its slow convergence affects the computational efficiency. Recently, much work was done to guarantee the acceleration of GIM in the literature. In this…

In this article we consider the widely used immersed finite element method (IFEM), in both explicit and implicit form, and its relationship to our more recent one-field fictitious domain method (FDM). We review and extend the formulation of…

This paper presents an immersed, isogeometric finite element framework to predict the response of multi-material, multi-physics problems with complex geometries using locally refined discretizations. To circumvent the need to generate…

We propose a Pretrained Finite Element Method (PFEM),a physics driven framework that bridges the efficiency of neural operator learning with the accuracy and robustness of classical finite element methods (FEM). PFEM consists of a physics…

For real matrices of full column-rank, we analyze the conditioning of several types of normal equations that are preconditioned by a randomized preconditioner computed in lower precision. These include symmetrically preconditioned normal…

We develop a cut finite element method for the Darcy problem on surfaces. The cut finite element method is based on embedding the surface in a three dimensional finite element mesh and using finite element spaces defined on the three…

A design optimization framework for process parameters of additive manufacturing based on finite element simulation is proposed. The finite element method uses a coupled thermomechanical model developed for fused deposition modeling from…

Many subsurface engineering applications involve tight-coupling between fluid flow, solid deformation, fracturing, and similar processes. To better understand the complex interplay of different governing equations, and therefore design…

In linear optimization, matrix structure can often be exploited algorithmically. However, beneficial presolving reductions sometimes destroy the special structure of a given problem. In this article, we discuss structure-aware…

In material science, models are derived to predict emergent material properties (e.g. elasticity, strength, conductivity) and their relations to processing conditions. A major drawback is the calibration of model parameters that depend on…

In the analysis of composite materials with heterogeneous microstructures, full resolution of the heterogeneities using classical numerical approaches can be computationally prohibitive. This paper presents a micromechanics-enhanced finite…

We introduce a new paradigm for immersed finite element and isogeometric methods based on interpolating function spaces from an unfitted background mesh into Lagrange finite element spaces defined on a foreground mesh that captures the…

Methodologies for reducing the design-space dimensionality in shape optimization have been recently developed based on unsupervised machine learning methods. These methods provide reduced dimensionality representations of the design space,…

We present and analyze a preconditioned conjugate gradient method (PCG) for solving spatial network problems. Primarily, we consider diffusion and structural mechanics simulations for fiber based materials, but the methodology can be…

We present a novel preconditioning technique for proximal optimization methods that relies on graph algorithms to construct effective preconditioners. Such combinatorial preconditioners arise from partitioning the graph into forests. We…