Numerical Approximation of the Multi-term Time-space Fractional Bloch-Torrey Equations on Irregular Convex Domains

2018 ◽  
Author(s):  
Fawang Liu ◽  
Libo Feng ◽  
Vo Anh
Keyword(s):  
Numerical Approximation ◽  
Convex Domains ◽  
Time Space

scholarly journals A novel unstructured mesh finite element method for solving the time-space fractional wave equation on a two-dimensional irregular convex domain

2017 ◽  
Vol 20 (2) ◽  
Author(s):  
Wenping Fan ◽  
Fawang Liu ◽  
Xiaoyun Jiang ◽  
Ian Turner
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Unstructured Mesh ◽  
The Finite Element Method ◽  
Galerkin Finite Element Method ◽  
Convex Domains ◽  
Galerkin Finite Element ◽  
Time Space ◽  
Structured Mesh ◽  
Element Method

AbstractMost existing research on applying the finite element method to discretize space fractional operators is studied on regular domains using either uniform structured triangular meshes, or quadrilateral meshes. Since many practical problems involve irregular convex domains, such as the human brain or heart, which are difficult to partition well with a structured mesh, the existing finite element method using the structured mesh is less efficient. Research on the finite element method using a completely unstructured mesh on an irregular domain is of great significance. In this paper, a novel unstructured mesh finite element method is developed for solving the time-space fractional wave equation on a two-dimensional irregular convex domain. The novel unstructured mesh Galerkin finite element method is used to discretize in space and the Crank-Nicholson scheme is used to discretize the Caputo time fractional derivative. The implementation of the unstructured mesh Crank-Nicholson Galerkin method (CNGM) is detailed and the stability and convergence of the numerical scheme are analyzed. Numerical examples are presented to verify the theoretical analysis. To highlight the ability of the proposed unstructured mesh Galerkin finite element method, a comparison of the unstructured mesh with the structured mesh in the implementation of the numerical scheme is conducted. The proposed numerical method using an unstructured mesh is shown to be more effective and feasible for practical applications involving irregular convex domains.

scholarly journals An advanced meshless approach for the high-dimensional multi-term time-space-fractional PDEs on convex domains

2021 ◽  
Author(s):  
X. G. Zhu ◽  
Y. F. Nie ◽  
J. G. Wang ◽  
Z. B. Yuan
Keyword(s):  
High Dimensional ◽  
Convex Domains ◽  
Time Space ◽  
Fractional Pdes

Time-Space Synesthesia: An Event-Related Brain Potential (ERP) Study

2007 ◽  
Author(s):  
Ursina Teuscher ◽  
David Brang ◽  
Lee Edwards ◽  
Marguerite McQuire ◽  
Vilayanur S. Ramachandran ◽  
...  
Keyword(s):  
Brain Potential ◽  
Time Space

The Time-Space Distribution Characteristics and Safety Improvement Measures of Traffic Accidents on Mountainous Expressways

CICTP 2020 ◽  
2020 ◽  
Author(s):  
Bi-Jiang Tian ◽  
Cheng-Yu Hu ◽  
Meng Zhang ◽  
Song Yue ◽  
Zhi-Neng Li
Keyword(s):  
Traffic Accidents ◽  
Space Distribution ◽  
Distribution Characteristics ◽  
Time Space ◽  
Safety Improvement ◽  
Improvement Measures
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