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The parallel solution of large scale non-linear programming problems, which arise for example from the discretization of non-linear partial differential equations, is a highly demanding task. Here, a novel solution strategy is presented,…
In this work, we present scalable balancing domain decomposition by constraints methods for linear systems arising from arbitrary order edge finite element discretizations of multi-material and heterogeneous 3D problems. In order to enforce…
Efficient algorithms for the solution of partial differential equations on parallel computers are often based on domain decomposition methods. Schwarz preconditioners combined with standard Krylov space solvers are widely used in this…
For a general formulation of linearised hybrid inverse problems in impedance tomography, the qualitative properties of the solutions are analysed. Using an appropriate scalar pseudo-differential formulation, the problems are shown to permit…
Multi-sector capacity expansion models play a crucial role in energy planning by providing decision support for policymaking in technology development. To ensure reliable support, these models require high technological, spatial, and…
Many real-world applications are addressed through a linear least-squares problem formulation, whose solution is calculated by means of an iterative approach. A huge amount of studies has been carried out in the optimization field to…
In this work, we generalize the numerical approach to Gaudin models developed earlier by us to degenerate systems showing that their treatment is surprisingly convenient from a numerical point of view. In fact, high degeneracies not only…
Rotation-based Post-Training Quantization (PTQ) has emerged as a promising solution for mitigating activation outliers in the quantization of Large Language Models (LLMs). Global rotation methods achieve inference efficiency by fusing…
Using a deterministic framework allows us to estimate a function with the purpose of interpolating data in spatial statistics. Radial basis functions are commonly used for scattered data interpolation in a d-dimensional space, however,…
In this paper we develop and analyse domain decomposition methods for linear systems of equations arising from conforming finite element discretisations of positive Maxwell-type equations. Convergence of domain decomposition methods rely…
Having in mind the modelling of marble degradation under chemical pollutants, e.g.~the sulfation process, we consider governing nonlinear diffusion equations and their numerical approximation.The space domain of a computation is the…
A new algorithm for solving large-scale convex optimization problems with a separable objective function is proposed. The basic idea is to combine three techniques: Lagrangian dual decomposition, excessive gap and smoothing. The main…
The paper describes a sparse direct solver for the linear systems that arise from the discretization of an elliptic PDE on a two dimensional domain. The scheme decomposes the domain into thin subdomains, or ``slabs'' and uses a two-level…
We investigate the application of the additive overlapping Schwarz domain decomposition method as a preconditioner for the large sparse linear systems arising in graph-based nonlinear least-squares problems, specifically the pose-graph…
Decentralized optimization algorithms are important in different contexts, such as distributed optimal power flow or distributed model predictive control, as they avoid central coordination and enable decomposition of large-scale problems.…
This paper presents a deep learning-based de-homogenization method for structural compliance minimization. By using a convolutional neural network to parameterize the mapping from a set of lamination parameters on a coarse mesh to a…
We consider the demixing problem of two (or more) high-dimensional vectors from nonlinear observations when the number of such observations is far less than the ambient dimension of the underlying vectors. Specifically, we demonstrate an…
We introduce a generalized framework for studying higher-order versions of the multiscale method known as Localized Orthogonal Decomposition. Through a suitable reformulation, we are able to accommodate both conforming and nonconforming…
We shall derive and propose several efficient overlapping domain decomposition methods for solving some typical linear inverse problems, including the identiffication of the flux, the source strength and the initial temperature in second…
This paper proposes a robust, high-precision positioning methodology to address localization failures arising from complex background interference in large-scale flight navigation and the computational inefficiency inherent in conventional…