Related papers: Multilevel correction type of adaptive finite elem…
This paper details the development and application of an $h$-adaptive finite element method for the numerical solution of the \textit{Falkner-Skan equation}. A posteriori error estimation governs the adaptivity of the mesh, specifically the…
We consider a finite element method for elliptic equation with heterogeneous and possibly high-contrast coefficients based on primal hybrid formulation. A space decomposition as in FETI and BDCC allows a sequential computations of the…
In this paper, we propose a novel $hr$-adaptive finite element method, enhanced by neural networks, for parabolic equations. The main challenge of the conventional $h$-adaptive finite element method is interpolating the finite element…
Methods for solving scientific computing and inference problems, such as kernel- and neural network-based approaches for partial differential equations (PDEs), inverse problems, and supervised learning tasks, depend crucially on the choice…
We present an adaptive finite element method for the incompressible Navier--Stokes equations based on a standard splitting scheme (the incremental pressure correction scheme). The presented method combines the efficiency and simplicity of a…
Recently, some hypergraph-based methods have been proposed to deal with the problem of model fitting in computer vision, mainly due to the superior capability of hypergraph to represent the complex relationship between data points. However,…
Algorithms that promise to leverage resources of quantum computers efficiently to accelerate the finite element method have emerged. However, the finite element method is usually incorporated into a high-level numerical scheme which allows…
In this paper, a novel adaptive finite element method is proposed to solve the Kohn-Sham equation based on the moving mesh (nonnested mesh) adaptive technique and the augmented subspace method. Different from the classical self-consistent…
Fourth-order differential equations play an important role in many applications in science and engineering. In this paper, we present a three-field mixed finite-element formulation for fourth-order problems, with a focus on the effective…
This paper is a follow-up to a previous work where we defined and generated the set of all possible compromises of multilevel multiobjective linear programming problems (ML-MOLPP). In this paper, we introduce a new algorithm to solve…
In this work, we present an adaptive unfitted finite element scheme that combines the aggregated finite element method with parallel adaptive mesh refinement. We introduce a novel scalable distributed-memory implementation of the resulting…
Semi-infinite programming can be used to model a large variety of complex optimization problems. The simple description of such problems comes at a price: semi-infinite problems are often harder to solve than finite nonlinear problems. In…
This paper is concerned with the value function approach to multiobjective bilevel optimization which exploits a lower level frontier-type mapping in order to replace the hierarchical model of two interdependent multiobjective optimization…
We combine the adaptive and multilevel approaches to the BDDC and formulate a method which allows an adaptive selection of constraints on each decomposition level. We also present a strategy for the solution of local eigenvalue problems in…
A finite element methodology for large classes of variational boundary value problems is defined which involves discretizing two linear operators: (1) the differential operator defining the spatial boundary value problem; and (2) a Riesz…
When modeling scientific and industrial problems, geometries are typically modeled by explicit boundary representations obtained from computer-aided design software. Unfitted (also known as embedded or immersed) finite element methods offer…
In this work, we deal with the problem of computing a comprehensive front of efficient solutions in multi-objective portfolio optimization problems in presence of sparsity constraints. We start the discussion pointing out some weaknesses of…
We introduce generalised finite difference methods for solving fully nonlinear elliptic partial differential equations. Methods are based on piecewise Cartesian meshes augmented by additional points along the boundary. This allows for…
Detectability of failures of linear programming (LP) decoding and its potential for improvement by adding new constraints motivate the use of an adaptive approach in selecting the constraints for the LP problem. In this paper, we make a…
Chemical accuracy serves as an important metric for assessing the effectiveness of the numerical method in Kohn--Sham density functional theory. It is found that to achieve chemical accuracy, not only the Kohn--Sham wavefunctions but also…