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A HIGHER-ORDER MULTISCALE METHOD FOR THE WAVE EQUATION

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arXiv 2023年

作者： Krumbiegel, Felix Maier, Roland Institute for Applied and Numerical Mathematics Karlsruhe Institute of Technology Englerstr. 2 Karlsruhe76131 Germany

MSC Codes 65M12, 65M60, 35L05In this paper we propose a multiscale method for the acoustic wave equation in highly oscillatory media. We use a higher-order extension of the localized orthogonal decomposition method combined with a higher-order time stepping scheme and present rigorous a-priori error estimates in the energy-induced norm. We find that in the very general setting without additional assumptions on the coefficient beyond boundedness, arbitrary orders of convergence cannot be expected but that increasing the polynomial degree may still considerably reduce the size of the error. Under additional regularity assumptions, higher orders can be obtained as well. numerical examples are presented that confirm the theoretical results. Copyright © 2023, The Authors. All rights reserved.

关键词： Wave equations

ISO-FLUCS:symmetrization of optofluidic manipulations in quasi-isothermal micro-environments

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eLight 2023年第1期3卷 105-121页

作者： Antonio Minopoli Susan Wagner Elena Erben Weida Liao Iliya D.Stoev Eric Lauga Moritz Kreysing Max-Planck-Institute of Molecular Cell Biology and Genetics DresdenGermany Department of Applied Mathematics and Theoretical Physics University of CambridgeCambridgeUK Center for Systems Biology Dresden DresdenGermany Institute of Biological and Chemical Systems-Biological Information Processing Karlsruhe Institute of TechnologyKarlsruheGermany

Recently,it has been demonstrated that thermoviscous flows can be used for a range of fine micromanipulations,such as moving the cytoplasm of cells and developing embryos,intracellular rheology,and femtonewton-range force *** flows,also known as focused-light-induced cytoplasmic streaming(FLUCS),are induced by mid-infrared laser scanning of a temperature spot through the ***,localized laser scanning can inflict temperature perturbations of several Kelvins on the sample,potentially eliciting unspecific biological *** this study,we demonstrate how exploiting symmetry relations during laser scanning effectively disentangles laser heating and flow *** introduce flow-neutral scan sequences that use dynamic photothermal stimuli and spatiotemporal symmetry relations of scanning bridging up to three distinct time *** leverage further insights from a recently published analytical model of flow fields to present quasi-homogenous temperature distributions that leave flow lines and their local and directed character largely *** present practical,intuitive solutions through predesigned sets of scan lines with near isothermal distributions and demonstrate that they are sufficient to generate and control flows in Caenorhabditis elegans embryos on a magnitude well in excess of endogenous flow *** results enable the separation of two previously tightly linked classes of physical stimuli,introduce a new,even less invasive standard for performing FLUCS perturbations,and pave the way for new unexplored avenues in the fields of soft matter and biomedicine.

关键词： quasi environments symmetry

Simulation of Particle-Agglomerate Transport in a Particle Filter using Lattice Boltzmann Methods

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Simulation of Particle-Agglomerate Transport in a Particle F...

22nd International Stuttgart Symposium, ISSYM 2022

作者： Hafen, Nicolas Krause, Mathias J. Dittler, Achim Gas Particle Systems Karlsruhe Institute of Technology Karlsruhe76131 Germany Lattice Boltzmann Research Group Karlsruhe Institute of Technology Karlsruhe76131 Germany Institute of Mechanical Process Engineering and Mechanics Karlsruhe Institute of Technology Karlsruhe76131 Germany Institute for Applied and Numerical Mathematics Karlsruhe Institute of Technology Karlsruhe76131 Germany Karlsruhe Institute of Technology Karlsruhe Germany

ISBN: (纸本)9783658370107

Wall-flow filters are used as particle filters in the exhaust gas after treatment of combustion engines. Soot is deposited in the filter and removed from it by regeneration through oxidation. However, an inert portion (ash) remains in the filter and forms different deposition patterns. Those patterns affect the separation efficiency as well as the overall pressure drop. The formation of deposition patterns is caused by rearrangement processes during regeneration, which result from the break-up of the particle layer as well as the resuspension and transport of individual agglomerates. With the help of the Homogenized Lattice Boltzmann Method (HLBM), resolved particle simulations are carried out within the framework of the open source software OpenLB. This allows the forces acting on the agglomerates to be determined and detachment and transport processes to be modelled. The focus of the present work is on a detailed investigation of the flow-induced transport of individual particle-agglomerates. © Springer Fachmedien Wiesbaden GmbH, ein Teil von Springer Nature 2022.

关键词： Wall flow

numerical Homogenization by Continuous Super-Resolution

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arXiv 2024年

作者： Liu, Zhi-Song Maier, Roland Rupp, Andreas Lappeenranta–Lahti University of Technology [LUT Finland Institute for Applied and Numerical Mathematics Karlsruhe Institute of Technology [KIT Germany Department of Mathematics Saarland University Germany

Finite element methods typically require a high resolution to satisfactorily approximate micro and even macro patterns of an underlying physical model. This issue can be circumvented by appropriate numerical homogenization or multiscale strategies that are able to obtain reasonable approximations on under-resolved scales. In this paper, we study the implicit neural representation and propose a continuous super-resolution network as a numerical homogenization strategy. It can take coarse finite element data to learn both in-distribution and out-of-distribution high-resolution finite element predictions. Our highlight is the design of a local implicit transformer, which is able to learn multiscale features. We also propose Gabor wavelet-based coordinate encodings which can overcome the bias of neural networks learning low-frequency features. Finally, perception is often preferred over distortion so scientists can recognize the visual pattern for further investigation. However, implicit neural representation is known for its lack of local pattern supervision. We propose to use stochastic cosine similarities to compare the local feature differences between prediction and ground truth. It shows better performance on structural alignments. Our experiments show that our proposed strategy achieves superior performance as an in-distribution and out-of-distribution super-resolution strategy. © 2024, CC BY.

关键词： Deep neural networks

Nonuniqueness of lattice Boltzmann schemes derived from finite difference methods

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arXiv 2024年

作者： Kummer, Eliane Simonis, Stephan Institute of Applied and Numerical Mathematics Karlsruhe Institute of Technology Englerstr. 2 Karlsruhe76131 Germany Lattice Boltzmann Research Group Karlsruhe Institute of Technology Englerstr. 2 Karlsruhe76131 Germany

Recently, the construction of finite difference schemes from lattice Boltzmann schemes has been rigorously analyzed [Bellotti et al. (2022), Numer. Math. 152, pp. 1–40]. It is thus known that any lattice Boltzmann scheme can be expressed in terms of a corresponding multi-step finite difference scheme on the conserved variables. In the present work, we provide counterexamples for the conjecture that any multi-step finite difference scheme has a unique lattice Boltzmann formulation. Based on that, we indicate the existence of equivalence classes for discretized relaxation *** Codes 65M06, 76M28 Copyright © 2024, The Authors. All rights reserved.

关键词： Equivalence classes

A NOVEL MODEL FOR DIRECT numerical SIMULATION OF SUSPENSION DYNAMICS WITH ARBITRARILY SHAPED CONVEX PARTICLES

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arXiv 2024年

作者： Marquardt, Jan E. Hafen, Nicolas Krause, Mathias J. Lattice Boltzmann Research Group Institute of Mechanical Process Engineering and Mechanics Karlsruhe Institute of Technology Karlsruhe76131 Germany Lattice Boltzmann Research Group Institute for Applied and Numerical Mathematics Karlsruhe Institute of Technology Karlsruhe76131 Germany

This study presents an innovative direct numerical simulation approach for complex particle systems with irregular shapes and large numbers. Using partially saturated methods, it accurately models arbitrary shapes, albeit at considerable computational cost when integrating a compatible contact model. The introduction of a novel parallelization strategy significantly improves the performance of the contact model, enabling efficient four-way coupled simulations. Through hindered settling studies, the criticality of the explicit contact model for maintaining simulation accuracy is highlighted, especially at high particle volume fractions and low Archimedes numbers. The feasibility of simulating thousands of arbitrarily shaped convex particles is demonstrated with up to 1934 surface-resolved particles. The study also confirms the grid independence and linear convergence of the method. It shows for the first time that cube swarms settle 13 to 26% slower than swarms of volume-equivalent spheres across different Archimedes numbers (500 to 2000) and particle volume fractions (10 to 30%). These findings emphasize the shape dependence of particle systems and suggest avenues for exploring their nuanced dynamics. Copyright © 2024, The Authors. All rights reserved.

关键词： Direct numerical simulation

A spectral decomposition method to approximate DtN maps in complicated waveguides

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arXiv 2022年

作者： Zhang, Ruming Institute of Applied and Numerical Mathematics Karlsruhe Institute of Technology Karlsruhe Germany

In this paper, we propose a new spectral decomposition method to simulate waves propagating in complicated waveguides. For the numerical solutions of waveguide scattering problems, an important task is to approximate the Dirichlet-to-Neumann map efficiently. From previous results, the physical solution can be decomposed into a family of generalized eigenfunctions, thus we can write the Dirichlet-to-Neumann map explicitly by these functions. From the exponential decay of the generalized eigenfunctions, we approximate the Dirichlet-to-Neumann (DtN) map by a finite truncation and the approximation is proved to converge exponentially. With the help of the truncated DtN map, the unbounded domain is truncated into a bounded one, and a variational formulation for the problem is set up in this bounded domain. The truncated problem is then solved by a finite element method. The error estimation is also provided for the numerical algorithm and numerical examples are shown to illustrate the efficiency of the algorithm. Copyright © 2022, The Authors. All rights reserved.

关键词： Eigenvalues and eigenfunctions

FINITE ELEMENT DISCRETIZATION OF NONLINEAR MODELS OF ULTRASOUND HEATING

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arXiv 2025年

作者： Careaga, Julio Dörich, Benjamin Nikolić, Vanja Department of Mathematics University of Bío-Bío Chile Institute for Applied and Numerical Mathematics Karlsruhe Institute of Technology Karlsruhe76149 Germany Department of Mathematics Radboud University Heyendaalseweg 135 Nijmegen6525 AJ Netherlands

Heating generated by high-intensity focused ultrasound waves is central to many emerging medical applications, including non-invasive cancer therapy and targeted drug delivery. In this study, we aim to gain a fundamental understanding of numerical simulations in this context by analyzing conforming finite element approximations of the underlying nonlinear models that describe ultrasound-heat interactions. These models are based on a coupling of a nonlinear Westervelt–Kuznetsov acoustic wave equation to the heat equation with a pressure-dependent source term. A particular challenging feature of the system is that the acoustic medium parameters may depend on the temperature. The core of our new arguments in the a prior error analysis lies in devising energy estimates for the coupled semi-discrete system that can accommodate the nonlinearities present in the model. To derive them, we exploit the parabolic nature of the system thanks to the strong damping present in the acoustic component. Theoretically obtained optimal convergence rates in the energy norm are confirmed by the numerical experiments. In addition, we conduct a further numerical study of the problem, where we simulate the propagation of acoustic waves in liver tissue for an initially excited profile and under high-frequency *** Codes 35L05, 35L72, 34A34 Copyright © 2025, The Authors. All rights reserved.

关键词： Ultrasonic waves

OPTIMAL W1,∞-ESTIMATES FOR AN ISOPARAMETRIC FINITE ELEMENT DISCRETIZATION OF ELLIPTIC BOUNDARY VALUE PROBLEMS

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Electronic Transactions on numerical Analysis 2022年 58卷

作者： Dörich, Benjamin Leibold, Jan Maier, Bernhard Institute for Applied and Numerical Mathematics Karlsruhe Institute of Technology Englerstr. 2 Karlsruhe76131 Germany

We consider an elliptic boundary value problem on a domain with regular boundary and discretize it with isoparametric finite elements of order k ≥ 1. We show optimal order of convergence of the isoparametric finite element solution in the W1,∞-norm. As an intermediate step, we derive stability and convergence estimates of optimal order k for a (generalized) Ritz map. Copyright © 2023, Kent State University.

关键词： Boundary value problems