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We present a space-time multigrid method based on tensor-product space-time finite element discretizations. The method is facilitated by the matrix-free capabilities of the {\ttfamily deal.II} library. It addresses both high-order…
In science and engineering, intelligent processing of complex signals such as images, sound or language is often performed by a parameterized hierarchy of nonlinear processing layers, sometimes biologically inspired. Hierarchical systems…
In this paper we analyse the convergence properties of two-level, W-cycle and V-cycle agglomeration-based geometric multigrid schemes for the numerical solution of the linear system of equations stemming from the lowest order…
Our goal is to present an elementary approach to the analysis and programming of sparse grid finite element methods. This family of schemes can compute accurate solutions to partial differential equations, but using far fewer degrees of…
A multigrid method is proposed in this paper to solve eigenvalue problems by the finite element method based on the shifted-inverse power iteration technique. With this scheme, solving eigenvalue problem is transformed to a series of…
In this paper, we introduce a powerful technique based on Leave-one-out analysis to the study of low-rank matrix completion problems. Using this technique, we develop a general approach for obtaining fine-grained, entrywise bounds for…
Model merging has attracted significant attention as a powerful paradigm for model reuse, facilitating the integration of task-specific models into a singular, versatile framework endowed with multifarious capabilities. Previous studies,…
In this work, we consider the modeling of inclusions in the material using an unfitted finite element method. In the unfitted methods, structured background meshes are used and only the underlying finite element space is modified to…
This paper presents a new fast iterative solver for large systems involving kernel matrices. Advantageous aspects of H2 matrix approximations and the multigrid method are hybridized to create the H2-MG algorithm. This combination provides…
Designing the topology of three-dimensional structures is a challenging problem due to its memory and time consumption. In this paper, we present a robust and efficient algorithm for solving large-scale 3D topology optimization problems.…
In this paper we analyse the convergence properties of V-cycle multigrid algorithms for the numerical solution of the linear system of equations arising from discontinuous Galerkin discretization of second-order elliptic partial…
Nonlinear least-squares problems are a special class of unconstrained optimization problems in which their gradient and Hessian have special structures. In this paper, we exploit these structures and proposed a matrix-free algorithm with a…
A novel finite element formulation for gradient-regularized damage models is presented which allows for the robust, efficient, and mesh-independent simulation of damage phenomena in engineering and biological materials. The paper presents a…
A type of parallel augmented subspace scheme for eigenvalue problems is proposed by using coarse space in the multigrid method. With the help of coarse space in multigrid method, solving the eigenvalue problem in the finest space is…
Stochastic gradient methods are scalable for solving large-scale optimization problems that involve empirical expectations of loss functions. Existing results mainly apply to optimization problems where the objectives are one- or two-level…
The goal of this primer is to provide a relatively short exposition of the basics of multigrid methods, simplified by focusing on fundamental concepts in a variational setting. This is done by way of a quadratic energy minimization…
We propose a new hybrid topology optimization algorithm based on multigrid approach that combines the parallelization strategy of CPU using OpenMP and heavily multithreading capabilities of modern Graphics Processing Units (GPU). In…
Firms earning prediction plays a vital role in investment decisions, dividends expectation, and share price. It often involves multiple tensor-compatible datasets with non-linear multi-way relationships, spatiotemporal structures, and…
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 consider the widely used continuous $\mathcal{Q}_{k}$-$\mathcal{Q}_{k-1}$ quadrilateral or hexahedral Taylor-Hood elements for the finite element discretization of the Stokes and generalized Stokes systems in two and three spatial…