We consider the time-dependent magnetic induction model as a step towards the resistive magnetohydrodynamics (MHD) model in incompressible media. Conforming nodal-based finite element (FE) approximations of the induct...
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ISBN:
(纸本)9783319399294;9783319399270
We consider the time-dependent magnetic induction model as a step towards the resistive magnetohydrodynamics (MHD) model in incompressible media. Conforming nodal-based finite element (FE) approximations of the induction model with Taylor-Hood type FE as well as equal-order FE for the magnetic field and the magnetic pseudo-pressure are investigated. We consider a stabilized nodalbased FEM for the numerical solution. Error estimates are given for the semidiscrete model in space. Finally, we present results for the magnetic flux expulsion problem.
Discretization of (linearized) convection-diffusion-reaction problems yields a large and sparse non symmetric linear system of equations, Ax = b In this work, we compare the computational behavior of the Induced Dimen...
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ISBN:
(纸本)9783319399294;9783319399270
Discretization of (linearized) convection-diffusion-reaction problems yields a large and sparse non symmetric linear system of equations, Ax = b In this work, we compare the computational behavior of the Induced Dimension Reduction method (IDR(s)) (Sonneveld and van Gijzen, SIAM J Sci Comput 31(2): 1035-1062, 2008), with other short-recurrences Krylov methods, specifically the Bi-Conjugate Gradient Method (Bi-CG) (Fletcher, Conjugate gradient methods for indefinite systems. In: Proceedings of the Dundee conference on numerical analysis, pp 73-89, 1976), restarted Generalized Minimal Residual (GMRES(m)) (Saad and Schultz, SIAM J Sci Stat Comput 7: 856-869, 1986), and Bi-Conjugate Gradient Stabilized method (Bi-CGSTAB) (van der Vorst, SIAM J Sci Stat Comput 13(2): 631-644, 1992).
The research and its outcomes presented in this collection focus on various aspects of high-performance computing (HPC) software and its development which is confronted with various challenges as today's supercomp...
ISBN:
(数字)9783319405285
ISBN:
(纸本)9783319405261
The research and its outcomes presented in this collection focus on various aspects of high-performance computing (HPC) software and its development which is confronted with various challenges as today's supercomputer technology heads towards exascale computing. The individual chapters address one or more of the research directions (1) computational algorithms, (2) system software, (3) application software, (4) data management and exploration, (5) programming, and (6) software tools. The collection thereby highlights pioneering research findings as well as innovative concepts in exascale software development that have been conducted under the umbrella of the priority programme "Software for Exascale Computing" (SPPEXA) of the German Research Foundation (DFG) and that have been presented at the SPPEXA Symposium, Jan 25-27 2016, in Munich. The book has an interdisciplinary appeal: scholars from computational sub-fields in computer science, mathematics, physics, or engineering will find it of particular interest.
igatools is a newly released library for operators assembly in isogeometric analysis. The library, which is object oriented designed and written in C++ 11, is general purpose, therefore it is not devoted to any specif...
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ISBN:
(数字)9783319233154
ISBN:
(纸本)9783319233154;9783319233147
igatools is a newly released library for operators assembly in isogeometric analysis. The library, which is object oriented designed and written in C++ 11, is general purpose, therefore it is not devoted to any specific application. In this paper we show that such a design makes igatools an effective tool in assembling isogeometric discretizations of sophisticated differential operators. This effectiveness will be demonstrated showing code snippets relating one-to-one with the operators written on paper. To embrace a wide audience, applications from nonlinear incompressible solid and fluid mechanics will be addressed. In both cases we are going to deal with mixed isogeometric formulations. The applicative nature of this paper will be stressed solving industrially relevant tests cases.
We investigate the application of a multiscale sparse grid finite element method for computing numerical solutions to a two-dimensional singularly perturbed convection-diffusion problem posed on the unit square. Typic...
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ISBN:
(纸本)9783319257273;9783319257259
We investigate the application of a multiscale sparse grid finite element method for computing numerical solutions to a two-dimensional singularly perturbed convection-diffusion problem posed on the unit square. Typically, sparse grid methods are constructed using a hierarchical basis (see, e.g., Bungartz and Griebel [1]). In our approach, the method is presented as a generalisation of the two-scale method described in Liu et al. [3], and is related to the combination technique outlined by Pflaum and Zhou [7]. We show that this method retains the same level of accuracy, in the energy norm, as both the standard Galerkin and two-scale methods. The computational cost associated with the method, however, is O(N logN), compared to O(N-2) and O(N-3/2) for the Galerkin and two-scale methods respectively.
In this paper we present a numerical wall function method for the simulation of isothermal flows with separation and reattachment based on the Reynolds averaged Navier-Stokes equations using an unstructured flow solve...
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ISBN:
(纸本)9783319257273;9783319257259
In this paper we present a numerical wall function method for the simulation of isothermal flows with separation and reattachment based on the Reynolds averaged Navier-Stokes equations using an unstructured flow solver. The method is applied to the one-equation turbulencemodel by Spalart and Allmaras and is implemented in OpenFOAM (R). For each wall node, a system of one-dimensional boundary-layer equations for the wall-parallel velocity component and for the turbulence quantity is integrated numerically on an embedded sub-grid in the near-wall region. The method is applied to the flow over a flat plate, over a backward facing step, and over a smoothly contoured ramp. The improvement of the results compared to universal wall functions become significant in case of separation and reattachment.
In this paper, we present an algorithm to simplify low-contributing atoms and generate quality T-meshes for multi-resolution biomolecular surfaces. The structure of biomolecules is first simplified using an error-boun...
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ISBN:
(数字)9783319233154
ISBN:
(纸本)9783319233154;9783319233147
In this paper, we present an algorithm to simplify low-contributing atoms and generate quality T-meshes for multi-resolution biomolecular surfaces. The structure of biomolecules is first simplified using an error-bounded atom elimination method. An extended cross field-based parameterization method is then developed to adapt the parametric line spacings to different surface resolutions. Moreover, an anisotropy defined from an input scalar field can also be achieved. From the parameterization results, we extract adaptive and anisotropic T-meshes for the further T-spline surface construction. Finally, a gradient flow-based method is developed to improve the T-mesh quality, with the anisotropy preserved in the quadrilateral elements. The effectiveness of the presented algorithm has been verified using several large biomolecular complexes.
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