Introduction. A fundamental paper in the theory of solving partial differential equations by iteration has been written by Frankel.1 In this paper Frankel discusses the Richardson and Liebmann procedures and their corresponding accelerated procedures. The latter are termed the extrapolated Liebmann and the second-order Richardson procedures. From his paper three disadvantages of the second-orde...

Experiments have been performed to assess the efficiency of mechanical mixers in destratifying water bodies. The effects of Reynolds number, physical scale, and Richardson number were all considered. The results demonstrated that the variation of mixing efficiency with Richardson number was well described by two different power-law regimes. At low Richardson numbers, the efficiency increased wi...

Littlewood-Richardson coefficients are the multiplicities in the tensor product decomposition of two irreducible representations of the general linear group GL(n,C). They have a wide variety of interpretations in combinatorics, representation theory and geometry. Mulmuley and Sohoni pointed out that it is possible to decide the positivity of Littlewood-Richardson coefficients in polynomial time...

mixed convection fluid flow and heat transfer of water-al2o3 nanofluid inside a lid-driven square cavity has been examined numerically in order to find the optimal distribution of discrete heat sources on the wall of a cavity. the effects of different heat source length, richardson number and grashof number on optimal heat source location has been investigated. moreover, the average nusselt num...

A posteriori error estimators are fundamental tools for providing confidence in the numerical computation of PDEs. To date, the main theories of a posteriori estimators have been developed largely in the finite element framework, for elliptic operators in the absence of disparate length scales. On the other hand, there is a strong interest in using grid refinement combined with Richardson extra...

A Fourier analysis is conducted in two-dimensional (2D) Cartesian geometry for the discreteordinates (SN) approximation of the neutron transport problem solved with Richardson iteration (Source Iteration) and Richardson iteration preconditioned with Transport Synthetic Acceleration (TSA), using the Parallel Block-Jacobi (PBJ) algorithm. The results for the un-accelerated algorithm show that con...

Various fields of science and engineering deal with dynamical systems that can be described by fractional partial differential equations (FPDE), for example, systems biology, chemistry and biochemistry applications due to anomalous diffusion effects in constrained environments. However, effective numerical methods and numerical analysis for FPDE are still in their infancy. In this paper, we con...

Cheng Gong, Geunsik Lee, Bin Shan, Eric M. Vogel, Robert M. Wallace, and Kyeongjae Cho Department of Materials Science and Engineering, The University of Texas at Dallas, Richardson, Texas 75080, USA Department of Electrical Engineering, The University of Texas at Dallas, Richardson, Texas 75080, USA Department of Physics, The University of Texas at Dallas, Richardson, Texas 75080, USA Departme...