A generic grid interface for parallel and adaptive scientific computing. Part II: implementation and tests in DUNE

Bastian, Peter; Blatt, Markus; Dedner, Andreas; Engwer, Christian; Klöfkorn, Robert; Kornhuber, Ralf; Ohlberger, Mario; Sander, Oliver

doi:10.1007/s00607-008-0004-9

Cited by 372 publications

(308 citation statements)

References 12 publications

Supporting

Mentioning

307

Contrasting

Order By: Relevance

“…4 For more details we refer to the cited paper. Hence we may set our fiber orientation density to the orientation distribution function q(θ) = ODF (θ).…”

Section: Fiber Density Qmentioning

confidence: 99%

“…While all necessary data, i.e. the diffusion tensor D T and the volume fraction of tissue fibers Q, are computed in advance from the DTI measurements using C++ and the Armadillo linear algebra library [55], we implemented the simulation of the PDE via the numerical framework DUNE [7,5,4,3]. The coefficients and the drift term depend on time and space, so we expect time dependent regions of the computational domain that are dominated by the diffusion term and others dominated by the drift term.…”

Section: Numerical Simulationsmentioning

confidence: 99%

See 1 more Smart Citation

A Multiscale Modeling Approach to Glioma Invasion with Therapy

Hunt

Surulescu

2016

Vietnam J. Math.

View full text Add to dashboard Cite

show abstract

“…4 For more details we refer to the cited paper. Hence we may set our fiber orientation density to the orientation distribution function q(θ) = ODF (θ).…”

Section: Fiber Density Qmentioning

confidence: 99%

Section: Numerical Simulationsmentioning

confidence: 99%

A Multiscale Modeling Approach to Glioma Invasion with Therapy

Hunt

Surulescu

2016

Vietnam J. Math.

View full text Add to dashboard Cite

show abstract

“…Each of the local problems on the subdomains is solved by 50 iterations of a linear multigrid which leads to numerically exact solutions. For the implementation we used the numerics environment DUNE [6]. Figure 4 shows that, as on the continuous level in Theorem 1, one obtains convergence if the damping parameter θ ∈ (0, 1) is below a threshold θ max , and one observes optimal convergence rates ρ opt for a certain θ opt .…”

Section: Parameter Studies For the Dirichlet-neumann Methodsmentioning

confidence: 99%

Convergence Behaviour of Dirichlet–Neumann and Robin Methods for a Nonlinear Transmission Problem

Berninger

Kornhuber

Sander

2010

Lecture Notes in Computational Science and Engineering

View full text Add to dashboard Cite

Summary. We investigate Dirichlet-Neumann and Robin methods for a quasilinear elliptic transmission problem in which the nonlinearity changes discontinuously across two subdomains. In one space dimension we obtain convergence theorems by extending known results from the linear case. They hold both on the continuous and on the discrete level. From the proofs one can infer mesh-independence of the convergence rates for the Dirichlet-Neumann method, but not for the Robin method. In two space dimensions we consider numerical examples which demonstrate that the theoretical results might be extended to higher dimensions. Moreover, we investigate the asymptotic convergence behaviour for fine mesh sizes quantitatively. We observe a good agreement with many known linear results, which is remarkable in view of the nonlinear character of the problem.

show abstract

“…Numerics Environment (DUNE) [20]. The coupled problem (free-flow domain, porous-medium domain and interface) is written in the following operator form…”

Section: -2mentioning

confidence: 99%

Numerical modelling of evaporation in a ceramic layer in the tape casting process

Jabbari

Jambhekar

Hattel

et al. 2016

AIP Conference Proceedings

View full text Add to dashboard Cite

Abstract. Evaporation of water from a ceramic layer is a key phenomenon in the drying process for the manufacturing of tape cast ceramics. This process contains mass, momentum and energy exchange between the porous medium and the freeflow region. In order to analyze such interaction processes, a Representative Elementary Volume (REV)-scale model concept is presented for coupling non-isothermal multi-phase compositional porous-media flow and single-phase compositional laminar free-flow. The preliminary results show the typical expected evaporation behaviour from a porous medium initially saturated with water, and its transport to the free-flow region according to the existent results from the literature.

show abstract

A generic grid interface for parallel and adaptive scientific computing. Part II: implementation and tests in DUNE

Cited by 372 publications

References 12 publications

A Multiscale Modeling Approach to Glioma Invasion with Therapy

A Multiscale Modeling Approach to Glioma Invasion with Therapy

Convergence Behaviour of Dirichlet–Neumann and Robin Methods for a Nonlinear Transmission Problem

Numerical modelling of evaporation in a ceramic layer in the tape casting process

Contact Info

Product

Resources

About