.png){kind=icon}
返回
Convex optimization-based structure-preserving filter for multidimensional finite element simulations
.png){kind=icon}
OA
AI
DOI：10.1016/j.jcp.2023.112364.png)
.png){kind=icon}
.png){kind=icon}
分享.png){kind=icon}
收藏
摘要
En 中文
In simulation sciences, capturing the real-world problem features as accurately as possible is desirable. Methods popular for scientific simulations such as the finite element method (FEM) and finite volume method (FVM) use piecewise polynomials to approximate various characteristics of a problem, such as the concentration profile and the temperature distribution across the domain. Polynomials are prone to creating artifacts such as Gibbs oscillations while capturing a complex profile. An efficient and accurate approach must be applied to deal with such inconsistencies to obtain accurate simulations. This often entails dealing with negative values for the concentration of chemicals, exceeding a percentage value over 100, and other such problems. We consider these inconsistencies in the context of partial differential equations (PDEs). We propose an innovative filter based on convex optimization to deal with the inconsistencies observed in polynomial-based simulations. In two or three spatial dimensions, additional complexities are involved in solving the problems related to structure preservation. We present the construction and application of a structure-preserving filter with a focus on multidimensional PDEs. Methods used such as the Barycentric interpolation for polynomial evaluation at arbitrary points in the domain and an optimized root-finder to identify points of interest, improve the filter efficiency, usability, and robustness. Lastly, we present numerical experiments in 2D and 3D using discontinuous Galerkin formulation and demonstrate the filter's efficacy to preserve the desired structure. As a real-world application, implementation of the mathematical biology model involving platelet aggregation and blood coagulation has been reviewed and the issues around FEM implementation of the model are resolved by applying the proposed structure-preserving filter.
Keyword:
Structure preservation
Convex optimization
Finite element methods
Partial differential equations
AI总结
对已上传原文的论文进行重点信息的提取，主要内容包括：简要概述、研究摘要、背景介绍、关键亮点、图文解析、展望与总结。
期刊
IF:
3.8
论文数:
1.6W
被引数:
7.4W
机构
引用论文
.png){kind=icon}
Direct Reaction of Silicon with α−ω Dichloroalkanes: Direct Formation of Dichlorosilacyclopentane
PREAI
分享收藏STRUCTURE-PRESERVING NONLINEAR FILTERING FOR CONTINUOUS AND DISCONTINUOUS GALERKIN SPECTRAL/HP ELEMENT METHODS连续和不连续GALERKIN谱/HP元方法的保结构非线性滤波
OAAI
OAAI分享收藏High-order local maximum principle preserving (MPP) discontinuous Galerkin finite element method for the transport equation输运方程的高阶局部极大值保持 (MPP) 间断Galerkin有限元方法OAAI
OAAI分享收藏Nektar plus plus : An open-source spectral/hp element frameworkNektar plus plus: 一个开源的spectral/hp元素框架OAAI
OAAI分享收藏POSITIVITY PRESERVING LIMITERS FOR TIME-IMPLICIT HIGHER ORDER ACCURATE DISCONTINUOUS GALERKIN DISCRETIZATIONS时间隐式高阶精确不连续GALERKIN离散化的正性保留限制器OAAI
OAAI分享收藏分享收藏
查看更多内容