A partition of unity finite element method for computational diffusion MRI

DOI10.1016/j.jcp.2018.08.039zbMath1416.65356OpenAlexW2889223833WikidataQ129312375 ScholiaQ129312375MaRDI QIDQ2002246

Johan Hoffman, Jing-Rebecca Li, Johan Jansson, Van-Dang Nguyen

Publication date: 11 July 2019

Published in: Journal of Computational Physics (Search for Journal in Brave)

Full work available at URL: http://hdl.handle.net/20.500.11824/863

zbMATH Keywords

interface conditionsBloch-Torrey equationpartition of unity finite element methodcomputational diffusion magnetic resonance imagingweak pseudoperiodic conditions

Mathematics Subject Classification ID

Biomedical imaging and signal processing (92C55) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Software, source code, etc. for problems pertaining to numerical analysis (65-04)

Related Items (1)

Fourier Representation of the Diffusion MRI Signal Using Layer Potentials

Uses Software

• RKC
• FEniCS
• Unicorn
• FEniCS-HPC

Cites Work

• A finite elements method to solve the Bloch-Torrey equation applied to diffusion magnetic resonance imaging
• A uniformly well-conditioned, unfitted Nitsche method for interface problems
• Computational homogenization based on a weak format of micro-periodicity for RVE-problems
• Automated solution of differential equations by the finite element method. The FEniCS book
• Convergence properties of the Runge-Kutta-Chebyshev method
• The partition of unity finite element method: basic theory and applications
• RKC: An explicit solver for parabolic PDEs
• Unicorn: parallel adaptive finite element simulation of turbulent flow and fluid-structure interaction for deforming domains and complex geometry
• A cut finite element method for a Stokes interface problem
• Über ein Variationsprinzip zur Lösung von Dirichlet-Problemen bei Verwendung von Teilräumen, die keinen Randbedingungen unterworfen sind. (On a variational principle for solving Dirichlet problems less boundary conditions using subspaces)
• Framework for Massively Parallel Adaptive Finite Element Computational Fluid Dynamics on Tetrahedral Meshes
• A Time Integration Algorithm for Structural Dynamics With Improved Numerical Dissipation: The Generalized-α Method
• Nitsche's method for interface problems in computa-tional mechanics
• Toward realization of computational homogenization in practice

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