Computers & Mathematics with Applications

Journal: Computers & Mathematics with Applications

Abbreviation

Comput. math. appl.

Publisher

Elsevier

ISSN

0898-1221
0097-4943
1873-7668

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Publications 1 - 10 of 15

Non-periodic Molecular Dynamics simulations of coarse grained lipid bilayer in water
Kotsalis, E.M.; Hanasaki, I.; Walther, Jens Honoré; et al. (2010)
Computers & Mathematics with Applications
Parallel MIC(0) preconditioning of 3D elliptic problems discretized by Rannacher–Turek finite elements
Arbenz, P.; Margenov, S.; Vutov, Y. (2008)
Computers & Mathematics with Applications
Nektar++: Design and implementation of an implicit, spectral/hp element, compressible flow solver using a Jacobian-free Newton Krylov approach
Yan, Zhen-Guo; Pan, Yu; Castiglioni, Giacomo; et al. (2021)
Computers & Mathematics with Applications ~ Development and Application of Open-source Software for Problems with Numerical PDEs
At high Reynolds numbers the use of explicit in time compressible flow simulations with spectral/hp element discretization can become significantly limited by time step. To alleviate this limitation we extend the capability of the spectral/hp element open-source software framework, Nektar++, to include an implicit discontinuous Galerkin compressible flow solver. The integration in time is carried out by a singly diagonally implicit Runge–Kutta method. The non-linear system arising from the implicit time integration is iteratively solved by the Jacobian-free Newton Krylov (JFNK) method. A favorable feature of the JFNK approach is its extensive use of the explicit operators available from the previous explicit in time implementation. The functionalities of different building blocks of the implicit solver are analyzed from the point of view of software design and placed in appropriate hierarchical levels in the C++ libraries. In the detailed implementation, the contributions of different parts of the solver to computational cost, memory consumption and programming complexity are also analyzed. A combination of analytical and numerical methods is adopted to simplify the programming complexity in forming the preconditioning matrix. The solver is verified and tested using cases such as manufactured compressible Poiseuille flow, Taylor–Green vortex, turbulent flow over a circular cylinder at Re=3900 and shock wave boundary-layer interaction. The results show that the implicit solver can speed-up the simulations while maintaining good simulation accuracy.
Guaranteed error bounds and local indicators for adaptive solvers using stabilised space–time IgA approximations to parabolic problems
Langer, Ulrich; Matculevich, Svetlana; Repin, Sergey (2019)
Computers & Mathematics with Applications
Exponential convergence of the hp-DGFEM for diffusion problems
Wihler, T.P.; Frauenfelder, P.; Schwab, C. (2003)
Computers & Mathematics with Applications
Higher order Quasi-Monte Carlo integration for Bayesian PDE Inversion
Dick, Josef; Gantner, Robert N.; Le Gia, Quoc T.; et al. (2019)
Computers & Mathematics with Applications
Coupling finite elements and auxiliary sources
Casati, Daniele; Hiptmair, Ralf (2019)
Computers & Mathematics with Applications
Analysis of a stabilization-free quadrilateral Virtual Element for 2D linear elasticity in the Hu-Washizu formulation
Cremonesi, Massimiliano; Lamperti, Andrea; Lovadina, Carlo; et al. (2024)
Computers & Mathematics with Applications
The Virtual Element Method (VEM) for the elasticity problem is considered in the framework of the Hu-Washizu variational formulation. In particular, a couple of low-order schemes presented in [1], are studied for quadrilateral meshes. The methods under consideration avoid the need of the stabilization term typical of the VEM, due to the introduction of a suitable projection on higher-order polynomials. The schemes are proved to be stable and optimally convergent in a compressible regime, including the case where highly distorted (even non-convex) meshes are employed.
Determining optimal multilevel Monte Carlo parameters with application to fault tolerance
Pauli, Stefan; Arbenz, Peter (2015)
Computers & Mathematics with Applications
Second-kind boundary integral equations for electromagnetic scattering at composite objects
Claeys, Xavier; Hiptmair, Ralf; Spindler, Elke (2017)
Computers & Mathematics with Applications

Publications 1 - 10 of 15

Journal: Computers & Mathematics with Applications

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