检索结果-内蒙古大学图书馆

Algebraic multigrid methods based on element preconditioning

INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS 2001年第4期78卷 575-598页

作者： Haase, G Langer, U Reitzinger, S Schöberl, J Institute for Analysis and Computational Mathematics Department of Computational Mathematics and Optimization Special Research Program (SFB) F013 Numerical and Symbolic Scientific Computing

This paper presents a new algebraic multigrid (AMG) solution strategy for large linear systems with a sparse matrix arising from a finite element discretization of some self-adjoint, second order, scalar, elliptic partial differential equation. The AMG solver is based on Ruge/Stuben's method. Ruge/Stuben's algorithm is robust for M-matrices, but unfortunately the "region of robustness" between symmetric positive definite M-matrices and general symmetric positive definite matrices is very fuzzy. For this reason the so-called element preconditioning technique is introduced in this paper. This technique aims at the construction of an M-matrix that is spectrally equivalent to the original stiffness matrix. This is done by solving small restricted optimization problems. AMG applied to the spectrally equivalent M-matrix instead of the original stiffness matrix is then used as a preconditioner in the conjugate gradient method for solving the original problem. The numerical experiments show the efficiency and the robustness of the new preconditioning method for a wide class of problems including problems with anisotropic elements.

关键词： finite element equations algebraic multigrid element preconditioning technique preconditioned conjugate gradient method

来源：评论

学校读者我要写书评

暂无评论

BPS2025 - Simulations of deformation-dependent signaling at the plasma membrane and the nuclear envelope

引用

Biophysical Journal 2025年第3期124卷 143a-143a页

作者： Emmet A. Francis Einollah Sarikhani Vrund Patel Dhivya P. Meganathan Marie E. Rognes Zeinab Jahed Padmini Rangamani Department of Pharmacology University of California San Diego La Jolla CA USA Department of Nanoengineering University of California San Diego La Jolla CA USA Department of Numerical Analysis and Scientific Computing Simula Research Laboratory Oslo Norway

来源：评论

学校读者我要写书评

暂无评论

Preprocessing for 2D FE-BE domain decomposition methods

引用

computing and Visualization in Science 1999年第1期2卷 25-35页

作者： Haase, Gundolf Kuhn, Michael Institute for Analysis and Comp. Math. Johannes Kepler University Linz A-4040 Linz Austria SFB 'Numerical and Scientific Computing' Johannes Kepler University Linz A-4040 Linz Austria

The non-overlapping Domain Decomposition (DD) method is a powerful tool for the coupling of Finite Element (FE) and Boundary Element (BE) methods. Moreover it provides a natural basis for constructing efficient parallel solvers. However, both, the efficiency and the robustness of DD-solvers depends heavily on the underlying decomposition of the domain of interest into subdomains. In this paper, we introduce the Adaptive Domain Decomposition Preprocessor ADDPre which realizes an automatic decomposition of the computational domain into p subdomains, where p is the number of processors to be used. We discuss the codes being involved, the algorithms which they are based on and the data-formats being used for describing the decomposition of the problem. numerical examples, demonstrating the performance of the preprocessor are presented. © 1999 Springer-Verlag.

关键词： Domain decomposition methods

来源：评论

学校读者我要写书评

暂无评论

Adjoint error estimation for stochastic collocation methods 1

引用

2nd Workshop on Sparse Grids and Applications, SGA 2012

作者： Schieche, Bettina Lang, Jens Numerical Analysis and Scientific Computing Department of Mathematics Technische Universität Darmstadt Dolivostr. 15 Darmstadt64293 Germany Numerical Analysis and Scientific Computing Department of Mathematics and Graduate School of Computational Engineering Technische Universität Darmstadt Dolivostr. 15 Darmstadt64293 Germany

ISBN: (数字)9783319045375

ISBN: (纸本)9783319045368

This paper deals with partial differential equations with random input data. An efficient way of solving such problems is adaptive stochastic collocation on sparse grids. For higher efficiency and a better understanding of the method, we derive adjoint error estimates for nonlinear stochastic solution functionals. The resulting adjoint problem also involves random parameters and can be treated by stochastic collocation as well. Only a few adjoint evaluations are required in order to estimate the deterministic error, while the stochastic error requires much more effort to be detected. To overcome these substantial additional costs, we suggest to replace the adjoint problem by a reduced model and demonstrate the applicability of the approach for nonlinear solution functionals and up to nine random dimensions. © Springer International Publishing Switzerland 2014.

关键词： Errors

来源：评论

学校读者我要写书评

暂无评论

Author Correction: Spatial modeling algorithms for reactions and transport in biological cells

NATURE COMPUTATIONAL SCIENCE

引用

NATURE COMPUTATIONAL SCIENCE 2025年第2期5卷 185-185页

作者： Francis, Emmet A. Laughlin, Justin G. Dokken, Jorgen S. Finsberg, Henrik N. T. Lee, Christopher T. Rognes, Marie E. Rangamani, Padmini Department of Pharmacology University of California San Diego School of Medicine La Jolla CA USA Department of Mechanical and Aerospace Engineering University of California San Diego La Jolla CA USA Computational Engineering Division Lawrence Livermore National Laboratory Livermore CA USA Department of Molecular Biology University of California San Diego La Jolla CA USA Department of Numerical Analysis and Scientific Computing Simula Research Laboratory Oslo Norway K. G. Jebsen Centre for Brain Fluid Research University of Oslo Oslo Norway Department of Computational Physiology Simula Research Laboratory Oslo Norway

来源：评论

学校读者我要写书评

暂无评论

Uncertainty quantification for thermo-convective Poiseuille flow using stochastic collocation

Uncertainty quantification for thermo-convective Poiseuille ...

引用

作者： Schieche, Bettina Lang, Jens Graduate School of Computational Engineering Center of Smart Interfaces Numerical Analysis and Scientific Computing Department of Mathematics Dolivostrasse 15 64293 Darmstadt Germany

Simulations become more reliable if they include random effects. One way to express uncertainties in the describing parameters are correlated random fields. Typically, the resulting problem is a partial differential equation (PDE) with random parameters. These additional, stochastic dimensions can be discretised either by spectral methods or stochastic collocation. The aim of this work is to analyse effects of an uncertain heating condition for plane Poiseuille flow by means of an adaptive, anisotropic stochastic collocation method. Additionally, we are interested in how the heat exchange can be improved by small surface variations. We show that the fluctuations of the resulting flow continuously depend on the input fluctuations. Furthermore, we can find specific surface structures that improve the heat exchange. Copyright © 2014 Inderscience Enterprises Ltd.

关键词： Stochastic systems

来源：评论

学校读者我要写书评

暂无评论

Modeling stochastic eye tracking data: A comparison of quantum generative adversarial networks and Markov models

Modeling stochastic eye tracking data: A comparison of quant...

引用

2024 Genetic and Evolutionary Computation Conference Companion, GECCO 2024 Companion

作者： Bhandari, Shailendra Lencastre, Pedro Lind, Pedro Department of Computer Science OsloMet - Oslo Metropolitan University OsloN-0130 Norway Simula Research Laboratory Numerical Analysis and Scientific Computing Oslo0164 Norway

ISBN: (纸本)9798400704956

We explore the use of quantum generative adversarial networks QGANs for modeling eye movement velocity data. We assess whether the advanced computational capabilities of QGANs can enhance the modeling of complex stochastic distribution beyond the traditional mathematical models, particularly the Markov model. The findings indicate that while QGANs demonstrate potential in approximating complex distributions, the Markov model consistently outperforms in accurately replicating the real data distribution. This comparison underlines the challenges and avenues for refinement in time series data generation using quantum computing techniques. It emphasizes the need for further optimization of quantum models to better align with real-world data characteristics. © 2024 is held by the owner/author(s).

关键词： Generative adversarial networks

来源：评论

学校读者我要写书评

暂无评论

Learning Place Cell Representations and Context-Dependent Remapping 38

Learning Place Cell Representations and Context-Dependent Re...

引用

38th Conference on Neural Information Processing Systems, NeurIPS 2024

作者： Pettersen, Markus Rogge, Frederik Lepperød, Mikkel Elle Department of Numerical Analysis and Scientific Computing Simula Research Laboratory Kristian Augusts Gate 23 Oslo Norway Department of Biosciences University of Oslo Blinderveien 31 Oslo Norway

Hippocampal place cells are known for their spatially selective firing patterns, which has led to the suggestion that they encode an animal's location. However, place cells also respond to contextual cues, such as smell. Furthermore, they have the ability to remap, wherein the firing fields and rates of cells change in response to changes in the environment. How place cell responses emerge, and how these representations remap is not fully understood. İn this work, we propose a similarity-based objective function that translates proximity in space, to proximity in representation. We show that a neural network trained to minimize the proposed objective learns place-like representations. We also show that the proposed objective is easily extended to include other sources of information, such as context information, in the same way. When trained to encode multiple contexts, networks learn distinct representations, exhibiting remapping behaviors between contexts. The proposed objective is invariant to orthogonal transformations. Such transformations of the original trained representation (e.g. rotationsİ, therefore yield new representations distinct from the original, without explicit relearning, akin to remapping. Our findings shed new light on the formation and encoding properties of place cells, and also demonstrate an interesting case of representational reuse. © 2024 Neural information processing systems foundation. All rights reserved.

关键词：

来源：评论

学校读者我要写书评

暂无评论

THE MODELLING ERROR IN MULTI-DIMENSIONAL TIME-DEPENDENT SOLUTE TRANSPORT MODELS

arXiv

引用

arXiv 2023年

作者： Masri, Rami Zeinhofer, Marius Kuchta, Miroslav Rognes, Marie E. Department of Numerical Analysis and Scientific Computing Simula Research Laboratory Norway

Starting from full-dimensional models of solute transport, we derive and analyze multi-dimensional models of time-dependent convection, diffusion, and exchange in and around pulsating vascular and perivascular networks. These models are widely applicable for modelling transport in vascularized tissue, brain perivascular spaces, vascular plants and similar environments. We show the existence and uniqueness of solutions to both the full- and the multi-dimensional equations under suitable assumptions on the domain velocity. Moreover, we quantify the associated modelling errors by establishing a-priori estimates in evolving Bochner spaces. In particular, we show that the modelling error decreases with the characteristic vessel diameter and thus vanishes for infinitely slender vessels. numerical tests in idealized geometries corroborate and extend upon our theoretical *** Codes 35K45, 65G99, 65J08, 65M15, 92-10 © 2023, CC BY-NC-SA.

关键词： Solute transport

来源：评论

学校读者我要写书评

暂无评论

SCALABLE APPROXIMATION AND SOLVERS FOR IONIC ELECTRODIFFUSION IN CELLULAR GEOMETRIES

arXiv

引用

arXiv 2024年

作者： Benedusi, Pietro Ellingsrud, Ada J. Herlyng, Halvor Rognes, Marie E. Department for Numerical Analysis and Scientific Computing Simula Research Laboratory Oslo Norway

The activity and dynamics of excitable cells are fundamentally regulated and moderated by extracellular and intracellular ion concentrations and their electric potentials. The increasing availability of dense reconstructions of excitable tissue at extreme geometric detail pose a new and clear scientific computing challenge for computational modelling of ion dynamics and transport. In this paper, we design, develop and evaluate a scalable numerical algorithm for solving the time-dependent and nonlinear KNP-EMI equations describing ionic electrodiffusion for excitable cells with an explicit geometric representation of intracellular and extracellular compartments and interior interfaces. We also introduce and specify a set of model scenarios of increasing complexity suitable for benchmarking. Our solution strategy is based on an implicit-explicit discretization and linearization in time, a mixed finite element discretization of ion concentrations and electric potentials in intracellular and extracellular domains, and an algebraic multigrid-based, inexact block-diagonal preconditioner for GMRES. numerical experiments with up to 108 unknowns per time step and up to 256 cores demonstrate that this solution strategy is robust and scalable with respect to the problem size, time discretization and number of *** Codes 65F10, 65N30, 65N55, 68U20, 68W10, 92-08, 92C20 © 2024, CC BY-SA.

关键词： Electric potential

来源：评论

学校读者我要写书评

暂无评论

建议与咨询留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

时间限定

文献类型

馆藏选择

核心期刊

语言

文献类型

帮助

文字说明：

检索规则说明：

检索范例：

分类表

所选分类

限定检索结果

文献类型

馆藏范围

日期分布

学科分类号

主题

机构

作者

语言

请选择保存的检索档案：

请选择收藏分类：

通借通还

建议与咨询 留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

时间限定

文献类型

馆藏选择

核心期刊

语言

文献类型

帮助

文字说明：

检索规则说明：

检索范例：

分类表

所选分类

限定检索结果

文献类型

馆藏范围

日期分布

学科分类号

主题

机构

作者

语言

请选择保存的检索档案： 新增检索档案 确定 取消

请选择收藏分类： 新增自定义分类 确定 取消

通借通还

建议与咨询留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

请选择保存的检索档案：

请选择收藏分类：