DIRK Schemes with High Weak Stage Order

Runge-Kutta time-stepping methods in general suffer from order reduction: the observed order of convergence may be less than the formal order when applied to certain stiff problems. Order reduction can be avoided by using methods with high stage order. However, diagonally-implicit Runge-Kutta (DIRK) schemes are limited to low stage order. In this paper we explore a weak stage order criterion, which for initial boundary value problems also serves to avoid order reduction, and which is compatible with a DIRK structure. We provide specific DIRK schemes of weak stage order up to 3, and demonstrate their performance in various examples.Comment: 10 pages, 5 figure

A temporally adaptive hybridized discontinuous Galerkin method for time-dependent compressible flows

The potential of the hybridized discontinuous Galerkin (HDG) method has been recognized for the computation of stationary flows. Extending the method to time-dependent problems can, e.g., be done by backward difference formulae (BDF) or diagonally implicit Runge-Kutta (DIRK) methods. In this work, we investigate the use of embedded DIRK methods in an HDG solver, including the use of adaptive time-step control. Numerical results demonstrate the performance of the method for both linear and nonlinear (systems of) time-dependent convection-diffusion equations

Fractional-Order Modelling in Modelica

open2siPollok, Alexander; Zimmer, Dirk; Casella, FrancescoPollok, ALEXANDER JOSEF; Zimmer, Dirk; Casella, Francesc

A Letter to A. C. Van Raalte from His Son, Ben

A letter to A. C. Van Raalte from his son, Ben, who gives him the bad news that brother Dirk has been wounded and his right arm amputated. Ben suggests that his father come down and take Dirk home. Dirk is making good recovery, however. Dirk, while out riding, chanced upon a group of rebel soldiers who tried to take him prisoner. As Dirk spurred his horse suddenly, he was shot, but escaped from the enemy.https://digitalcommons.hope.edu/vrp_1860s/1261/thumbnail.jp

[Review of] Dirk Hoerder, ed. The Immigrant Labor Press in North America, 1840s-70s (Three volumes)

Dirk Hoerder has undertaken a truly mammoth task -- the identification, analysis, and the location of surviving collections of the immigrant labor press published in the United States and Canada from the mid-nineteenth century to the present. For the most part his efforts have been successful. Without question he has provided researchers interested in the American immigrant experience or American labor history with a valuable research tool

Reseña: Ex(tra)territorial. Reassessing Territory in Literature, Culture and Languages / Les Territoires littéraires, culturels et linguistiques en question

Ressenya de Didier Lassalle i Dirk Weissmann (eds.): Ex(tra)territorial. Reassessing Territory in Literature, Culture and Languages. Les Territoires littéraires, culturels et linguistiques en questionReview of Didier Lassalle and Dirk Weissmann (eds.): Ex(tra)territorial. Reassessing Territory in Literature, Culture and Languages. Les Territoires littéraires, culturels et linguistiques en questionReseña de Didier Lassalle y Dirk Weissmann (eds.): Ex(tra)territorial. Reassessing Territory in Literature, Culture and Languages. Les Territoires littéraires, culturels et linguistiques en question

Support-based lower bounds for the positive semidefinite rank of a nonnegative matrix

The positive semidefinite rank of a nonnegative $(m\times n)$-matrix~$S$ is the minimum number~$q$ such that there exist positive semidefinite $(q\times q)$-matrices $A_1,\dots,A_m$, $B_1,\dots,B_n$ such that S(k,\ell) = \mbox{tr}(A_k^* B_\ell). The most important, lower bound technique for nonnegative rank is solely based on the support of the matrix S, i.e., its zero/non-zero pattern. In this paper, we characterize the power of lower bounds on positive semidefinite rank based on solely on the support.Comment: 9 page

A Letter of Dirk Van Raalte to His Parents in Holland

A letter of Dirk Van Raalte to his parents in Holland, reporting on his experiences in the army. Dirk continues to work in the hospital. The camp is about one-half mile out of town. Dirk assures his mother that he is getting enough to eat.https://digitalcommons.hope.edu/vrp_1860s/1161/thumbnail.jp