Related papers: Robust and parallel scalable iterative solutions f…
Hierarchical spatial models are very flexible and popular for a vast array of applications in areas such as ecology, social science, public health, and atmospheric science. It is common to carry out Bayesian inference for these models via…
Fourth-order variational inequalities are encountered in various scientific and engineering disciplines, including elliptic optimal control problems and plate obstacle problems. In this paper, we consider additive Schwarz methods for…
Decision rules offer a rich and tractable framework for solving certain classes of multistage adaptive optimization problems. Recent literature has shown the promise of using linear and nonlinear decision rules in which wait-and-see…
We propose a two-scale finite element method designed for heterogeneous microstructures. Our approach exploits domain diffeomorphisms between the microscopic structures to gain computational efficiency. By using a conveniently constructed…
We extend a distributed finite element method built upon model order reduction to arbitrary polynomial degree using a hybrid Nitsche scheme. The new method considerably simplifies the transformation of the finite element system to the…
We present scalable iterative solvers and preconditioning strategies for Hybridizable Discontinuous Galerkin (HDG) discretizations of partial differential equations (PDEs) on graphics processing units (GPUs). The HDG method is implemented…
The solution of linear systems of equations is a central task in a number of scientific and engineering applications. In many cases the solution of linear systems may take most of the simulation time thus representing a major bottleneck in…
In this thesis, the numerical solution of three different classes of problems have been studied. Specifically, new techniques have been proposed and their theoretical analysis has been performed, accompanied by a wide set of numerical…
The Multilevel Monte Carlo (MLMC) method has proven to be an effective variance-reduction statistical method for Uncertainty Quantification (UQ) in Partial Differential Equation (PDE) models, combining model computations at different levels…
This paper presents a high-accuracy higher-order multiscale method for solving multi-continuum problems in in highly heterogeneous media. First, microscopic unit cell functions are defined, leading to the derivation of macroscopic…
Coupled nonlinear system of reaction-diffusion equations describing multi-component (species) interactions with heterogeneous coefficients is considered. Finite volume method based approximation for the space is used to construct…
This work presents a matrix-free finite element solver for finite-strain elasticity adopting an $hp$-multigrid preconditioner. Compared to classical algorithms relying on a global sparse matrix, matrix-free solution strategies significantly…
In this paper, we further investigate and refine the subspace-constrained preconditioning technique to enhance the theoretical and numerical convergence properties of randomized iterative methods for solving linear systems. In particular,…
This paper addresses the problem of parallelizing computations to study non-linear dynamics in large networks of non-locally coupled oscillators using heterogeneous computing resources. The proposed approach can be applied to a variety of…
Kernel methods are versatile tools for function approximation and surrogate modeling. In particular, greedy techniques offer computational efficiency and reliability through inherent sparsity and provable convergence. Inspired by the…
Cell blebs are protrusions of the cell membrane and can be instrumental for cell migration. We derive a continuum model for the mechanical and geometrical aspects of the onset of blebbing in terms of a force balance. It is abstract and…
In this paper we are concerned with restricted additive Schwarz with local impedance transformation conditions for a family of Helmholtz problems in two dimensions. These problems are discretized by the finite element method with conforming…
We present a deep learning-based iterative approach to solve the discrete heterogeneous Helmholtz equation for high wavenumbers. Combining classical iterative multigrid solvers and convolutional neural networks (CNNs) via preconditioning,…
Efficient solutions of large-scale, ill-conditioned and indefinite algebraic equations are ubiquitously needed in numerous computational fields, including multiphysics simulations, machine learning, and data science. Because of their…
We present a discontinuous finite element method for the shallow water equations which exploits high-resolution realistic bathymetry data without any regularity assumption, also in the case of high-order discretizations. We prove a number…