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Special Issue "Mesh Methods - Numerical Analysis and Experiments"
A special issue of Symmetry (ISSN 2073-8994).
Deadline for manuscript submissions: 31 December 2019.
Interests: boundary value problems with singularity, numerical methods in electrodynamics, hydrodynamics and theory of elasticity
Interests: Singular boundary value problems; integro-differential equations; high-order methods
Mathematical models of different natural processes are described by differential equations, systems of PDEs and integral equations. In most cases, the exact solution of such problems cannot be determined, so we have to use mesh methods to calculate an approximate solution using high performance computational complexes. These methods include the finite element method, the finite difference method, the finite volume method and combined methods.
In this Special Issue, we propose to publish qualitative works on theoretical studies of grid methods on approximation, stability, and convergence, as well as the results of numerical experiments confirming the effectiveness of the developed methods. New methods for boundary value problems with singularity, with a complex geometry of the domain boundary, and for non-linear equations are of particular interest. Articles concerning analysis of the numerical methods developed for the computation of mathematical models in different areas of applied science and engineering applications will be welcome.
As a rule, symmetry ideas are present in the computational schemes and make the process harmonious and effective.
Prof. Viktor A. Rukavishnikov
Prof. Pedro M. Lima
Prof. Ildar B. Badriev
Manuscript Submission Information
Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All papers will be peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.
Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Symmetry is an international peer-reviewed open access monthly journal published by MDPI.
Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 1400 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.
- finite element method
- difference method
- finite volume method
- numerical experiments
- numerical analysis
The below list represents only planned manuscripts. Some of these manuscripts have not been received by the Editorial Office yet. Papers submitted to MDPI journals are subject to peer-review.
MODIFIED MULTIGRID METHOD FOR THE NAVIER-STOKES EQUATIONS WITH THE HSS-SMOOTHERS
E. Andreeva, V. Bavin, T. Martynova, G. Muratova
A modification of the multigrid method (MGM) is considered for discretized systems of partial differential equations (PDEs) which arise from finite difference approximation of the incompressible Navier-Stokes equations. After discretization and linearization of the equations, systems of linear algebraic equations (SLAE) with a strongly non-Hermitian matrix is obtained. Hermitian and Skew-Hermitian Splitting (HSS) smoothers are used in the MGM for solving of the SLAE. Parallel algebraic multigrid method with GPGPU technology is used. Some numerical results are presented.