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We design an adaptive finite element method to approximate the solutions of quasi-linear elliptic problems. The algorithm is based on a Ka\v{c}anov iteration and a mesh adaptation step is performed after each linear solve. The method is…
An adaptive refinement strategy, based on an equilibrated flux a posteriori error estimator, is proposed in the context of defeaturing problems. Defeaturing consists of removing features from complex domains to simplify mesh generation and…
Hierarchical optimization refers to problems with interdependent decision variables and objectives, such as minimax and bilevel formulations. While various algorithms have been proposed, existing methods and analyses lack adaptivity in…
The development of efficient and accurate image reconstruction algorithms is one of the cornerstones of computed tomography. Existing algorithms for quantitative photoacoustic tomography currently operate in a two-stage procedure: First an…
An adaptive isogeometric method based on $d$-variate hierarchical spline constructions can be derived by considering a refine module that preserves a certain class of admissibility between two consecutive steps of the adaptive loop [6]. In…
The method of superposition is proposed in combination with a sparse $\ell_1$ optimisation algorithm with the aim of finding a sparse basis to accurately reconstruct the structural vibrations of a radiating object from a set of acoustic…
An algorithm is devised for solving minimization problems with equality constraints. The algorithm uses first-order derivatives of both the objective function and the constraints. The step is computed as a sum between a steepest-descent…
The development of nonlinear optimization algorithms capable of performing reliably in the presence of noise has garnered considerable attention lately. This paper advocates for strategies to create noise-tolerant nonlinear optimization…
In recent years, metamaterials have gained considerable attention as a promising material technology due to their unique properties and customizable design, distinguishing them from traditional materials. This article delves into the value…
The calculation of potential energy surfaces for quantum dynamics can be a time consuming task -- especially when a high level of theory for the electronic structure calculation is required. We propose an adaptive interpolation algorithm…
An efficient algorithm for adaptive kernel smoothing (AKS) of two-dimensional imaging data has been developed and implemented using the Interactive Data Language (IDL). The functional form of the kernel can be varied (top-hat, Gaussian…
In this work, we explore the use of operator splitting algorithms for solving regularized structural topology optimization problems. The context is the classical structural design problems (e.g., compliance minimization and compliant…
This article combines shape optimization and homogenization techniques by looking for the optimal design of the microstructure in composite materials and of scaffolds. The development of materials with specific properties is of huge…
One difficulty in developing numerical methods for hyperbolic systems of conservation laws is the fact that solutions often contain regions where much higher resolution is required than elsewhere in the domain, particularly since the…
The so-called Locally Resonant Acoustic Metamaterials (LRAM) are considered for the design of specifically engineered devices capable of stopping waves from propagating in certain frequency regions (bandgaps), this making them applicable…
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…
We present an algorithm for sound analysis and resynthesis with local automatic adaptation of time-frequency resolution. There exists several algorithms allowing to adapt the analysis window depending on its time or frequency location; in…
This article initiates the study of space-time adaptive mesh refinements for time-dependent boundary element formulations of wave equations. Based on error indicators of residual type, we formulate an adaptive boundary element procedure for…
The iterative nature of topology optimization, especially in combination with nonlinear state problems, often requires the solution of thousands of linear equation systems. Furthermore, due to the pixelated design representation, the use of…
Mitigating low-frequency noise is particularly challenging due to its limited natural attenuation. This study aims to design viscoelastic composite microstructures that achieve both low acoustic reflection and high internal damping by…