Related papers: Localized Orthogonal Decomposition Method with $H^…
We propose an discontinuous Galerkin local orthogonal decomposition multiscale method for convection-diffusion problems with rough, heterogeneous, and highly varying coefficients. The properties of the multiscale method and the…
In this paper we present a locally and dimension-adaptive sparse grid method for interpolation and integration of high-dimensional functions with discontinuities. The proposed algorithm combines the strengths of the generalised sparse grid…
This paper is dedicated to the study of the orthogonal decomposition of spatially and temporally distributed signals in fluid-structure interaction problems. First application is concerned with the analysis of wall-pressure distributions…
We devise and evaluate numerically a Hybrid High-Order (HHO) method for incremental associative plasticity with small deformations. The HHO method uses as discrete unknowns piecewise polynomials of order $k\ge1$ on the mesh skeleton,…
The evaluation of robustness and reliability of realistic structures in the presence of uncertainty involves costly numerical simulations with a very high number of evaluations. This motivates model order reduction techniques like the…
Super-resolution is an important but difficult problem in image/video processing. If a video sequence or some training set other than the given low-resolution image is available, this kind of extra information can greatly aid in the…
$L^1$ based optimization is widely used in image denoising, machine learning and related applications. One of the main features of such approach is that it naturally provide a sparse structure in the numerical solutions. In this paper, we…
In this work, a numerical simulation of 1D Burgers' equation is developed using finite difference method and a reduced order model (ROM) of the simulation is developed using proper orthogonal decomposition (POD). The objective of this work…
Multi-modal multi-objective optimization problems (MMMOPs) have multiple subsets within the Pareto-optimal Set, each independently mapping to the same Pareto-Front. Prevalent multi-objective evolutionary algorithms are not purely designed…
In the context of unfitted finite element discretizations the realization of high order methods is challenging due to the fact that the geometry approximation has to be sufficiently accurate. Recently a new unfitted finite element method…
Low rank orthogonal tensor approximation (LROTA) is an important problem in tensor computations and their applications. A classical and widely used algorithm is the alternating polar decomposition method (APD). In this article, an improved…
A finite element method for elliptic problems with discontinuous coefficients is presented. The discontinuity is assumed to take place along a closed smooth curve. The proposed method allows to deal with meshes that are not adapted to the…
This paper introduces a multifidelity formulation that reduces the computational cost of the proper orthogonal decomposition (POD) of a high-fidelity model by leveraging data from cheaper, lower-fidelity models. POD is a prevalent technique…
We present an algorithm which computes a cylindrical algebraic decomposition of a semialgebraic set using projection sets computed for each cell separately. Such local projection sets can be significantly smaller than the global projection…
We propose and analyze a new hybridizable discontinuous Galerkin (HDG) method for second-order elliptic problems. Our method is obtained by inserting the $L^2$-orthogonal projection onto the approximate space for a numerical trace into all…
Parameterized quantum circuits (PQCs) are ubiquitous in the design of hybrid quantum-classical algorithms. In this work, we propose an interpolation-based coordinate descent (ICD) method to address the parameter optimization problem in…
In this paper, we propose a model-driven method that reconstructs LoD-2 building models following a "decomposition-optimization-fitting" paradigm. The proposed method starts building detection results through a deep learning-based detector…
In this paper, we propose a model reduction method for solving multiscale elliptic PDEs with random coefficients in the multiquery setting using an optimization approach. The optimization approach enables us to construct a set of localized…
The modal decomposition techniques of proper orthogonal decomposition (POD) and dynamic mode decomposition (DMD) have become a common method for analysing the spatio-temporal coherence of dynamical systems. In particular, these techniques…
Reduced-order models are essential tools to deal with parametric problems in the context of optimization, uncertainty quantification, or control and inverse problems. The set of parametric solutions lies in a low-dimensional manifold (with…