68,837 research outputs found
Structures and waves in a nonlinear heat-conducting medium
The paper is an overview of the main contributions of a Bulgarian team of
researchers to the problem of finding the possible structures and waves in the
open nonlinear heat conducting medium, described by a reaction-diffusion
equation. Being posed and actively worked out by the Russian school of A. A.
Samarskii and S.P. Kurdyumov since the seventies of the last century, this
problem still contains open and challenging questions.Comment: 23 pages, 13 figures, the final publication will appear in Springer
Proceedings in Mathematics and Statistics, Numerical Methods for PDEs:
Theory, Algorithms and their Application
Dissipative stability theory for linear repetitive processes with application in iterative learning control
This paper develops a new set of necessary and sufficient conditions for the stability of linear repetitive processes, based on a dissipative setting for analysis. These conditions reduce the problem of determining whether a linear repetitive process is stable or not to that of checking for the existence of a solution to a set of linear matrix inequalities (LMIs). Testing the resulting conditions only requires compu- tations with matrices whose entries are constant in comparison to alternatives where frequency response computations are required
Thermophysical Phenomena in Metal Additive Manufacturing by Selective Laser Melting: Fundamentals, Modeling, Simulation and Experimentation
Among the many additive manufacturing (AM) processes for metallic materials,
selective laser melting (SLM) is arguably the most versatile in terms of its
potential to realize complex geometries along with tailored microstructure.
However, the complexity of the SLM process, and the need for predictive
relation of powder and process parameters to the part properties, demands
further development of computational and experimental methods. This review
addresses the fundamental physical phenomena of SLM, with a special emphasis on
the associated thermal behavior. Simulation and experimental methods are
discussed according to three primary categories. First, macroscopic approaches
aim to answer questions at the component level and consider for example the
determination of residual stresses or dimensional distortion effects prevalent
in SLM. Second, mesoscopic approaches focus on the detection of defects such as
excessive surface roughness, residual porosity or inclusions that occur at the
mesoscopic length scale of individual powder particles. Third, microscopic
approaches investigate the metallurgical microstructure evolution resulting
from the high temperature gradients and extreme heating and cooling rates
induced by the SLM process. Consideration of physical phenomena on all of these
three length scales is mandatory to establish the understanding needed to
realize high part quality in many applications, and to fully exploit the
potential of SLM and related metal AM processes
H2/H∞ output information-based disturbance attenuation for differential linear repetitive processes
Repetitive processes propagate information in two independent directions where the duration of one is finite. They pose control problems that cannot be solved by application of results for other classes of 2D systems. This paper develops controller design algorithms for differential linear processes, where information in one direction is governed by a matrix differential equation and in the other by a matrix discrete equation, in an H2/H∞ setting. The objectives are stabilization and disturbance attenuation, and the controller used is actuated by the process output and hence the use of a state observer is avoided
Efficient Explicit Time Stepping of High Order Discontinuous Galerkin Schemes for Waves
This work presents algorithms for the efficient implementation of
discontinuous Galerkin methods with explicit time stepping for acoustic wave
propagation on unstructured meshes of quadrilaterals or hexahedra. A crucial
step towards efficiency is to evaluate operators in a matrix-free way with
sum-factorization kernels. The method allows for general curved geometries and
variable coefficients. Temporal discretization is carried out by low-storage
explicit Runge-Kutta schemes and the arbitrary derivative (ADER) method. For
ADER, we propose a flexible basis change approach that combines cheap face
integrals with cell evaluation using collocated nodes and quadrature points.
Additionally, a degree reduction for the optimized cell evaluation is presented
to decrease the computational cost when evaluating higher order spatial
derivatives as required in ADER time stepping. We analyze and compare the
performance of state-of-the-art Runge-Kutta schemes and ADER time stepping with
the proposed optimizations. ADER involves fewer operations and additionally
reaches higher throughput by higher arithmetic intensities and hence decreases
the required computational time significantly. Comparison of Runge-Kutta and
ADER at their respective CFL stability limit renders ADER especially beneficial
for higher orders when the Butcher barrier implies an overproportional amount
of stages. Moreover, vector updates in explicit Runge--Kutta schemes are shown
to take a substantial amount of the computational time due to their memory
intensity
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