GAMM Mitteilungen最新文献

Regularizations of forward-backward parabolic PDEs 前后抛物线 PDE 的正则化

GAMM Mitteilungen Pub Date : 2024-10-21 DOI: 10.1002/gamm.202470001

Carina Geldhauser

引用次数: 0

Parallel two-scale finite element implementation of a system with varying microstructure 对具有不同微观结构的系统进行并行双尺度有限元计算

GAMM Mitteilungen Pub Date : 2024-10-20 DOI: 10.1002/gamm.202470005

Omar Lakkis, Adrian Muntean, Omar Richardson, Chandrasekhar Venkataraman

{"title":"Parallel two-scale finite element implementation of a system with varying microstructure","authors":"Omar Lakkis, Adrian Muntean, Omar Richardson, Chandrasekhar Venkataraman","doi":"10.1002/gamm.202470005","DOIUrl":"https://doi.org/10.1002/gamm.202470005","url":null,"abstract":"We propose a two-scale finite element method designed for heterogeneous microstructures. Our approach exploits domain diffeomorphisms between the microscopic structures to gain computational efficiency. By using a conveniently constructed pullback operator, we are able to model the different microscopic domains as macroscopically dependent deformations of a reference domain. This allows for a relatively simple finite element framework to approximate the underlying system of partial differential equations with a parallel computational structure. We apply this technique to a model problem where we focus on transport in plant tissues. We illustrate the accuracy of the implementation with convergence benchmarks and show satisfactory parallelization speed-ups. We further highlight the effect of the heterogeneous microscopic structure on the output of the two-scale systems. Our implementation (publicly available on GitHub) builds on the deal.II FEM library. Application of this technique allows for an increased capacity of microscopic detail in multiscale modeling, while keeping running costs manageable.","PeriodicalId":53634,"journal":{"name":"GAMM Mitteilungen","volume":"47 4","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-10-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/gamm.202470005","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142579678","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Low Mach number limit of a diffuse interface model for two-phase flows of compressible viscous fluids 可压缩粘性流体两相流扩散界面模型的低马赫数极限

GAMM Mitteilungen Pub Date : 2024-08-12 DOI: 10.1002/gamm.202470008

Helmut Abels, Yadong Liu, Šárka Nečasová

引用次数: 0

Mathematical analysis of a mesoscale model for multiphase membranes 多相膜中尺度模型的数学分析

GAMM Mitteilungen Pub Date : 2024-08-10 DOI: 10.1002/gamm.202470009

Jakob Fuchs, Matthias Röger

{"title":"Mathematical analysis of a mesoscale model for multiphase membranes","authors":"Jakob Fuchs, Matthias Röger","doi":"10.1002/gamm.202470009","DOIUrl":"https://doi.org/10.1002/gamm.202470009","url":null,"abstract":"In this article, we introduce a mesoscale continuum model for membranes made of two different types of amphiphilic lipids. The model extends work by Peletier and the second author (Arch. Ration. Mech. Anal. 193, 2009) for the one-phase case. We present a mathematical analysis of the asymptotic reduction to the macroscale when a key length parameter becomes arbitrarily small. We identify two main contributions in the energy: one that can be connected to bending of the overall structure and a second that describes the cost of the internal phase separations. We prove the <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>Γ</mi>\u0000 </mrow>\u0000 <annotation>$$ Gamma $$</annotation>\u0000 </semantics></math>-convergence towards a perimeter functional for the phase separation energy and construct, in two dimensions, recovery sequences for the convergence of the full energy towards a 2D reduction of the Jülicher–Lipowsky bending energy with a line tension contribution for phase separated hypersurfaces.","PeriodicalId":53634,"journal":{"name":"GAMM Mitteilungen","volume":"47 4","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/gamm.202470009","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142579620","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Robustness and exploration of variational and machine learning approaches to inverse problems: An overview 逆问题变分法和机器学习方法的稳健性和探索：综述

GAMM Mitteilungen Pub Date : 2024-08-07 DOI: 10.1002/gamm.202470003

Alexander Auras, Kanchana Vaishnavi Gandikota, Hannah Droege, Michael Moeller

引用次数: 0

Learning from small data sets: Patch-based regularizers in inverse problems for image reconstruction 从小型数据集中学习：图像重建逆问题中基于补丁的正则器

GAMM Mitteilungen Pub Date : 2024-08-07 DOI: 10.1002/gamm.202470002

Moritz Piening, Fabian Altekrüger, Johannes Hertrich, Paul Hagemann, Andrea Walther, Gabriele Steidl

{"title":"Learning from small data sets: Patch-based regularizers in inverse problems for image reconstruction","authors":"Moritz Piening, Fabian Altekrüger, Johannes Hertrich, Paul Hagemann, Andrea Walther, Gabriele Steidl","doi":"10.1002/gamm.202470002","DOIUrl":"https://doi.org/10.1002/gamm.202470002","url":null,"abstract":"The solution of inverse problems is of fundamental interest in medical and astronomical imaging, geophysics as well as engineering and life sciences. Recent advances were made by using methods from machine learning, in particular deep neural networks. Most of these methods require a huge amount of data and computer capacity to train the networks, which often may not be available. Our paper addresses the issue of learning from small data sets by taking patches of very few images into account. We focus on the combination of model-based and data-driven methods by approximating just the image prior, also known as regularizer in the variational model. We review two methodically different approaches, namely optimizing the maximum log-likelihood of the patch distribution, and penalizing Wasserstein-like discrepancies of whole empirical patch distributions. From the point of view of Bayesian inverse problems, we show how we can achieve uncertainty quantification by approximating the posterior using Langevin Monte Carlo methods. We demonstrate the power of the methods in computed tomography, image super-resolution, and inpainting. Indeed, the approach provides also high-quality results in zero-shot super-resolution, where only a low-resolution image is available. The article is accompanied by a GitHub repository containing implementations of all methods as well as data examples so that the reader can get their own insight into the performance.","PeriodicalId":53634,"journal":{"name":"GAMM Mitteilungen","volume":"47 4","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/gamm.202470002","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142579675","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Neural-network-based regularization methods for inverse problems in imaging 基于神经网络的成像逆问题正则化方法

GAMM Mitteilungen Pub Date : 2024-07-18 DOI: 10.1002/gamm.202470004

Andreas Habring, Martin Holler

引用次数: 0

Modeling of fluid-rigid body interaction in an electrically conducting fluid 导电流体中的流体-刚体相互作用模型

GAMM Mitteilungen Pub Date : 2024-07-17 DOI: 10.1002/gamm.202470012

Jan Scherz, Anja Schlömerkemper

引用次数: 0

Numerical simulation of endovascular treatment options for cerebral aneurysms 脑动脉瘤血管内治疗方案的数值模拟

GAMM Mitteilungen Pub Date : 2024-07-17 DOI: 10.1002/gamm.202370007

Martin Frank, Fabian Holzberger, Medeea Horvat, Jan Kirschke, Matthias Mayr, Markus Muhr, Natalia Nebulishvili, Alexander Popp, Julian Schwarting, Barbara Wohlmuth

{"title":"Numerical simulation of endovascular treatment options for cerebral aneurysms","authors":"Martin Frank, Fabian Holzberger, Medeea Horvat, Jan Kirschke, Matthias Mayr, Markus Muhr, Natalia Nebulishvili, Alexander Popp, Julian Schwarting, Barbara Wohlmuth","doi":"10.1002/gamm.202370007","DOIUrl":"https://doi.org/10.1002/gamm.202370007","url":null,"abstract":"Predicting the long-term success of endovascular interventions in the clinical management of cerebral aneurysms requires detailed insight into the patient-specific physiological conditions. In this work, we not only propose numerical representations of endovascular medical devices such as coils, flow diverters or Woven EndoBridge but also outline numerical models for the prediction of blood flow patterns in the aneurysm cavity right after a surgical intervention. Detailed knowledge about the postsurgical state then lays the basis to assess the chances of a stable occlusion of the aneurysm required for a long-term treatment success. To this end, we propose mathematical and mechanical models of endovascular medical devices made out of thin metal wires. These can then be used for fully resolved flow simulations of the postsurgical blood flow, which in this work will be performed by means of a Lattice Boltzmann method applied to the incompressible Navier–Stokes equations and patient-specific geometries. To probe the suitability of homogenized models, we also investigate poro-elastic models to represent such medical devices. In particular, we examine the validity of this modeling approach for flow diverter placement across the opening of the aneurysm cavity. For both approaches, physiologically meaningful boundary conditions are provided from reduced-order models of the vascular system. The present study demonstrates our capabilities to predict the postsurgical state and lays a solid foundation to tackle the prediction of thrombus formation and, thus, the aneurysm occlusion in a next step.","PeriodicalId":53634,"journal":{"name":"GAMM Mitteilungen","volume":"47 3","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/gamm.202370007","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142137869","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Coupled simulations and parameter inversion for neural system and electrophysiological muscle models 神经系统和肌肉电生理模型的耦合模拟和参数反演

GAMM Mitteilungen Pub Date : 2024-03-31 DOI: 10.1002/gamm.202370009

Carme Homs-Pons, Robin Lautenschlager, Laura Schmid, Jennifer Ernst, Dominik Göddeke, Oliver Röhrle, Miriam Schulte

{"title":"Coupled simulations and parameter inversion for neural system and electrophysiological muscle models","authors":"Carme Homs-Pons, Robin Lautenschlager, Laura Schmid, Jennifer Ernst, Dominik Göddeke, Oliver Röhrle, Miriam Schulte","doi":"10.1002/gamm.202370009","DOIUrl":"https://doi.org/10.1002/gamm.202370009","url":null,"abstract":"The functioning of the neuromuscular system is an important factor for quality of life. With the aim of restoring neuromuscular function after limb amputation, novel clinical techniques such as the agonist-antagonist myoneural interface (AMI) are being developed. In this technique, the residual muscles of an agonist-antagonist pair are (re-)connected via a tendon in order to restore their mechanical and neural interaction. Due to the complexity of the system, the AMI can substantially profit from in silico analysis, in particular to determine the prestretch of the residual muscles that is applied during the procedure and determines the range of motion of the residual muscle pair. We present our computational approach to facilitate this. We extend a detailed multi-X model for single muscles to the AMI setup, that is, a two-muscle-one-tendon system. The model considers subcellular processes as well as 3D muscle and tendon mechanics and is prepared for neural process simulation. It is solved on high performance computing systems. We present simulation results that show (i) the performance of our numerical coupling between muscles and tendon and (ii) a qualitatively correct dependence of the range of motion of muscles on their prestretch. Simultaneously, we pursue a Bayesian parameter inference approach to invert for parameters of interest. Our approach is independent of the underlying muscle model and represents a first step toward parameter optimization, for instance, finding the prestretch, to be applied during surgery, that maximizes the resulting range of motion. Since our multi-X fine-grained model is computationally expensive, we present inversion results for reduced Hill-type models. Our numerical results for cases with known ground truth show the convergence and robustness of our approach.","PeriodicalId":53634,"journal":{"name":"GAMM Mitteilungen","volume":"47 3","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/gamm.202370009","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142137878","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0