HIGH-ORDER EXPLICIT TIME-INTEGRATORS FOR DISCONTINUOUS GALERKIN DISCRETIZATIONS OF THE MAXWELL EQUATIONS

2012 ◽  
Vol 04 (01) ◽  
pp. 1250029
Author(s):  
H. FAHS ◽  
M. SAFA
Keyword(s):  
Discontinuous Galerkin ◽  
Large Scale ◽  
Formal Solution ◽  
High Order ◽  
Practical Implementation ◽  
Test Problems ◽  
Time Integrators ◽  
The Matrix ◽  
Long Time ◽  
Exponential Formula

We investigate the practical implementation of a high-order explicit time-stepping method based on polynomial approximations, for possible application to large-scale problems in electromagnetics. After the spatial discretization by a high-order discontinuous Galerkin method, we obtain a linear system of differential equations of the form, [Formula: see text], where [Formula: see text] is a matrix containing the spatial derivatives and t is the time variable. The formal solution can be written in terms of the matrix exponential, [Formula: see text], acting on some vectors. We introduce a general family of time-integrators based on the approximation of [Formula: see text] by Jacobi polynomial expansions. We discuss the efficient implementation of this technique, and based on some test problems, we compare the virtues and shortcomings of the algorithm. We also demonstrate how these schemes provide an efficient alternative to standard explicit integrators for computing solutions over long time intervals.

The Masteralloy Concept for Sintered Steels - New Impetus for a Classical Approach

2021 ◽  
Vol 42 ◽  
pp. 9-16
Author(s):  
Herbert Danninger ◽  
Raquel de Oro Calderon ◽  
Stefan Geroldinger ◽  
Christian Gierl-Mayer ◽  
John J. Dunkley
Keyword(s):  
Large Scale ◽  
Oxygen Affinity ◽  
Cost Effective ◽  
The Other ◽  
Water Atomization ◽  
The Matrix ◽  
Recent Developments ◽  
Long Time ◽  
Pressure Water ◽  
High Oxygen Affinity

Among the various alloying techniques used in powder metallurgy, the masteralloy concept has been known for a long time. However, its use for production of ferrous precision parts has been hampered by several obstacles such as poor output of the useful fine fractions, high tool wear and slow homogenization kinetics of the alloy elements in the matrix. On the other hand, the masteralloy concept is particularly interesting for introducing cost-effective alloy elements such as Cr, Mn and Si since the masteralloy approach at least alleviates the problems caused by the high oxygen affinity of these elements. In the present study it is shown that recent developments have given a boost to this classical concept, one of these developments being powder manufacturing by high pressure water atomization which dramatically increases the yield of fine masteralloy fractions. The other progress is availability of thermodynamic software that enables defining masteralloy compositions with low melting range and thus fast homogenization also at moderate sintering temperatures. Combined, these new developments open the door for implementation of the masteralloy route in large scale PM parts production.

scholarly journals Asynchronous communication in spectral-element and discontinuous Galerkin methods for atmospheric dynamics – a case study using the High-Order Methods Modeling Environment (HOMME-homme_dg_branch)

2016 ◽  
Vol 9 (8) ◽  
pp. 2881-2892 ◽  
Author(s):  
Benjamin F. Jamroz ◽  
Robert Klöfkorn
Keyword(s):  
Discontinuous Galerkin ◽  
Large Scale ◽  
Discontinuous Galerkin Methods ◽  
Spectral Element ◽  
Asynchronous Communication ◽  
High Order ◽  
Galerkin Methods ◽  
High Order Methods ◽  
Data Movement ◽  
Modeling Environment

Abstract. The scalability of computational applications on current and next-generation supercomputers is increasingly limited by the cost of inter-process communication. We implement non-blocking asynchronous communication in the High-Order Methods Modeling Environment for the time integration of the hydrostatic fluid equations using both the spectral-element and discontinuous Galerkin methods. This allows the overlap of computation with communication, effectively hiding some of the costs of communication. A novel detail about our approach is that it provides some data movement to be performed during the asynchronous communication even in the absence of other computations. This method produces significant performance and scalability gains in large-scale simulations.

scholarly journals IMPLEMENTATION OF HIGH-ORDER, DISCONTINUOUS GALERKIN TIME STEPPING FOR FRACTIONAL DIFFUSION PROBLEMS

2020 ◽  
Vol 62 (2) ◽  
pp. 121-147
Author(s):  
WILLIAM MCLEAN
Keyword(s):  
Discontinuous Galerkin ◽  
Fractional Order ◽  
Numerical Experiments ◽  
Time Integration ◽  
Fractional Diffusion ◽  
High Order ◽  
Practical Implementation ◽  
Time Stepping ◽  
Carry Over ◽  
Diffusion Problems

AbstractThe discontinuous Galerkin (DG) method provides a robust and flexible technique for the time integration of fractional diffusion problems. However, a practical implementation uses coefficients defined by integrals that are not easily evaluated. We describe specialized quadrature techniques that efficiently maintain the overall accuracy of the DG method. In addition, we observe in numerical experiments that known superconvergence properties of DG time stepping for classical diffusion problems carry over in a modified form to the fractional-order setting.

Symplectic interior penalty discontinuous Galerkin method for solving the seismic scalar wave equation

Geophysics ◽  
2019 ◽  
Vol 84 (3) ◽  
pp. T133-T145 ◽  
Author(s):  
Xijun He ◽  
Dinghui Yang ◽  
Xiao Ma ◽  
Yanjie Zhou
Keyword(s):  
Wave Equation ◽  
Discontinuous Galerkin ◽  
Discontinuous Galerkin Method ◽  
Time Integration ◽  
High Accuracy ◽  
High Order ◽  
Numerical Dispersion ◽  
Scalar Wave ◽  
Long Time

To improve the computational accuracy and efficiency of long-time wavefield simulations, we have developed a so-called symplectic interior penalty discontinuous Galerkin (IPDG) method for 2D acoustic equation. For the symplectic IPDG method, the scalar wave equation is first transformed into a Hamiltonian system. Then, the high-order IPDG formulations are introduced for spatial discretization because of their high accuracy and ease of dealing with computational domains with complex boundaries. The time integration is performed using an explicit third-order symplectic partitioned Runge-Kutta scheme so that it preserves the Hamiltonian structure of the wave equation in long-term simulations. Consequently, the symplectic IPDG method combines the advantages of discontinuous Galerkin method and the symplectic time integration. We investigate the properties of the method in detail for high-order spatial basis functions, including the stability criteria, numerical dispersion and dissipation relationships, and numerical errors. The analyses indicate that the symplectic SIPG method is nondissipative and retains low numerical dispersion. We also find that different symplectic IPDG methods have different convergence behaviors. It is indicated that using coarse meshes with a high-order method produces smaller errors and retains high accuracy. We have applied our method to simulate the scalar wavefields for different models, including layered models, a rough topography model, and the Marmousi model. The numerical results show that the symplectic IPDG method can suppress numerical dispersion effectively and provide accurate information on the wavefields. We also conduct a long-term experiment that verifies the capability of symplectic IPDG method for long-time simulations.

TO THE QUESTION OF RESPONSIBILITY FOR TORTURE IN THE RUSSIAN FEDERATION

2020 ◽  
Vol 10 (2) ◽  
pp. 103-106
Author(s):  
ASTEMIR ZHURTOV ◽  
Keyword(s):  
Human Rights ◽  
Russian Federation ◽  
Large Scale ◽  
Human Life ◽  
International Standards ◽  
World Community ◽  
The World ◽  
Long Time ◽  
Protection Of Human Rights ◽  
The Russian Federation

Cruel and inhumane acts that harm human life and health, as well as humiliate the dignity, are prohibited in most countries of the world, and Russia is no exception in this issue. The article presents an analysis of the institution of responsibility for torture in the Russian Federation. The author comes to the conclusion that the current criminal law of Russia superficially and fragmentally regulates liability for torture, in connection with which the author formulated the proposals to define such act as an independent crime. In the frame of modern globalization, the world community pays special attention to the protection of human rights, in connection with which large-scale international standards have been created a long time ago. The Universal Declaration of Human Rights and other international acts enshrine prohibitions of cruel and inhumane acts that harm human life and health, as well as degrade the dignity.Considering the historical experience of the past, these standards focus on the prohibition of any kind of torture, regardless of the purpose of their implementation.

Sign in / Sign up

Export Citation Format

Share Document