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A practical algorithm to minimize the overall error in FEM computations
Jie Liu, Henk M. Schuttelaars, Matthias Möller
Using the standard finite element method (FEM) to solve general partial differential equations, the round-off error is found to be proportional to , with the num…
Combining p-multigrid and multigrid reduced in time methods to obtain a scalable solver for Isogeometric Analysis
Roel Tielen, Matthias Möller, Cornelis Vuik
Isogeometric Analysis (IgA) has become a viable alternative to the Finite Element Method (FEM) and is typically combined with a time integration scheme within the method of lines f…
Towards Accuracy and Scalability: Combining Isogeometric Analysis with Deflation to Obtain Scalable Convergence for the Helmholtz Equation
Vandana Dwarka, Roel Tielen, Matthias Möller +1
Finding fast yet accurate numerical solutions to the Helmholtz equation remains a challenging task. The pollution error (i.e. the discrepancy between the numerical and analytical w…
The Role of PDE-Based Parameterization Techniques in Gradient-Based IGA Shape Optimization Applications
Jochen Hinz, Andrzej Jaeschke, Matthias Möller +1
This paper proposes a shape optimization algorithm based on the principles of Isogeometric Analysis (IGA) in which the parameterization of the geometry enters the problem formulati…
Balancing truncation and round-off errors in practical FEM: one-dimensional analysis
Jie Liu, Matthias Möller, Henk M. Schuttelaars
In finite element methods (FEMs), the accuracy of the solution cannot increase indefinitely because the round-off error increases when the number of degrees of freedom (DoFs) is la…
Isogeometric Analysis of the Gray-Scott Reaction-Diffusion Equations for Pattern Formation on Evolving Surfaces and Applications to Human Gyrification
Jochen Hinz, Joost van Zwieten, Matthias Möller +1
We propose a numerical scheme based on the principles of Isogeometric Analysis (IgA) for a geometrical pattern formation induced evolution of manifolds. The development is modelled…