166,956 research outputs found
[Report to Chief J. E. Curry, by an unknown author #1]
No full textReport to Chief J. E. Curry, by an unknown author. The report contains a list of officers who gave depositions to the United States Attorney
[Report to Chief J. E. Curry, by an unknown author #2]
No full textReport to Chief J. E. Curry, by an unknown author. The report contains a list of officers who gave depositions to the United States Attorney
BREEDEN RUNGE COMPANY
No full textTelegram from Breeden Runge Company to Geo. J. Read informing that due to the health condition of Mr. Breeden he will not be able to see him in Laredo. / Telegrama de Breeden Runge Company a Geo. J. Read informándole que por razones de salud el Sr. Breeden no lo podrá ver en Laredo
Philipp Otto Runge, Die Lehrstunde der Nachtigall
No full textGrave J. Philipp Otto Runge, Die Lehrstunde der Nachtigall. In: Bertsch M, Fleckner U, Howoldt J, Stolzenburg A, eds. Kosmos Runge. Der Morgen der Romantik [Kat. zur Ausst. der Hamburger Kunsthalle 2010/11]. München; In Press: 120-126
Efficient explicit time integration for the simulation of acoustic and electromagnetic waves
No full textThe efficient and accurate numerical simulation of time-dependent wave phenomena is of fundamental importance in acoustic, electromagnetic or seismic wave propagation.
Model problems describing wave propagation include the wave equation and Maxwell's equations, which we study in this work. Both models are partial differential equations in space and time. Following the method-of-lines approach we first discretize the two model problems in space using finite element methods (FEM) in their continuous or discontinuous form. FEM are increasingly popular in the presence of heterogeneous media or complex geometry due to their inherent flexibility: elements can be small precisely where small features are located, and larger elsewhere. Such a local mesh refinement, however, also imposes severe stability constraints on explicit time integration, as the maximal time-step is dictated by the smallest elements in the mesh. When mesh refinement is restricted to a small region, the use of implicit methods, or a very small time-step in the entire computational domain, are generally too high a price to pay.
Local time-stepping (LTS) methods alleviate that geometry induced stability restriction by dividing the elements into two distinct regions: the "coarse region" which contains the larger elements and is integrated in time using an explicit method, and the "fine region" which contains the smaller elements and is integrated in time using either smaller time-steps or an implicit scheme.
Here we first present LTS schemes based on explicit Runge-Kutta (RK) methods. Starting from classical or low-storage explicit RK methods, we derive explicit LTS methods of arbitrarily high accuracy.
We prove that the LTS-RKs(p) methods yield the same rate of convergence as the underlying RKs scheme. Numerical experiments with continuous and discontinuous Galerkin finite element discretizations corroborate the expected rates of convergence and illustrate the usefulness of these LTS-RK methods.
As a second method we propose local exponential Adams-Bashforth (LexpAB) schemes. Unlike LTS schemes, LexpAB methods overcome the severe stability restrictions caused by local mesh refinement not by integrating with a smaller time-step but by using the exact matrix exponential in the fine region. Thus, they present an interesting alternative to the LTS schemes. Numerical experiments in 1D and 2D confirm the expected order of convergence and demonstrate the versatility of the approach in cases of extreme refinement
To Runge approximation via quasiconformal folding
No full textRungejev aproksimacijski izrek je eden izmed osrednjih rezultatov kompleksne analize. Izrek nam pove, da lahko holomorfne funkcije na kompaktih aproksimiramo z racionalnimi preslikavami, ne zagotovi pa nam nadzora nad kritičnimi točkami teh racionalnih preslikav. Na začetku leta 2023 sta ameriška matematika C. J. Bishop in K. Lazebnik objavila članek, v katerem sta dokazala izboljšavo Rungejevega aproksimacijskega izreka, tako imanovano Runge+ aproksimacijo, ki nam da ta dodaten nadzor nad kritičnimi točkami. Dokaz izreka temelji na tehniki kvazikonformnega zgibanja, ki jo je leta 2015 razvil C. J. Bishop. V delu najprej predstavimo teorijo kvazikonfomrnih preslikav, nato izpeljemo kvazikonformno zgibanje, nazadnje pa dokažemo Runge+ aproksimacijo v primeru povezanih Rungejevih kompaktov.The Runge approximation theorem is one of the fundamental results of complex analysis. The theorem states that we can approximate holomorphic functions on compact sets using rational maps, but it doesn\u27t give us any control over the critical points of these rational maps. At the beginning of 2023, the American mathematicians C. J. Bishop and K. Lazebnik published a paper, where they proved an improved version of the Runge approximation theorem, the so-called Runge+ approximation, which does give us control over critical points. The proof is based on a technique called quasiconformal folding, developed by C. J. Bishop in 2015. In the thesis we first present the theory of quasiconformal maps, then derive quasiconformal folding and finally, we prove Runge+ approximation in the case of connected Runge compacts
Order conditions for partitioned Runge-Kutta methods
No full textsummary:We illustrate the use of the recent approach by P. Albrecht to the derivation of order conditions for partitioned Runge-Kutta methods for ordinary differential equations
Group photograph of Oscar Groeneveld, Ian Runge, J. E. Ritchie, Hon. R. E. Camm
No full textGroup photograph from left to right of Oscar Groeneveld, Ian Runge, J. E. Ritchie, Hon. R. E. Camm (former MLA Qld)
Construction of explicit and generalized Runge-Kutta formulas of arbitrary order with rational parameters
No full textsummary:In the article containing the algorithm of explicit generalized Runge-Kutta formulas of arbitrary order with rational parameters two problems occuring in the solution of ordinary differential equaitions are investigated, namely the determination of rational coefficients and the derivation of the adaptive Runge-Kutta method. By introducing suitable substitutions into the nonlinear system of condition equations one obtains a system of linear equations, which has rational roots. The introduction of suitable symbols enables the authors to generalize the Runge-Kutta formulas. The starting point for the construction of adaptive R. K. method was the consistent -stage R. K. formula. Finally, the S-stability of the ARK method is investigated
Implicit-explicit Runge-Kutta method for combustion simulation
No full textNew high order implicit-explicit Runge-Kutta methods have been developed and implemented into a finite volume code to solve the Navier-Stokes equations for reacting gas mixtures. The resulting nonlinear systems in each stage are solved by Newtons method. If only the chemistry is treated implicitly, the linear systems in each Newton iteration are simple and solved directly. If in addition certain convection or diffusion terms are treated implicitly as well, the sparse linear systems in each Newton iteration are solved by preconditioned GMRES. Numerical simulations of deflagration-to-detonation transition (DDT) show the potential of the new time integration for computaional combustion
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