An agglomeration-based massively parallel non-overlapping additive Schwarz preconditioner for high-order discontinuous Galerkin methods on polytopic grids

In this article we design and analyze a class of two-level non-overlapping additive Schwarz preconditioners for the solution of the linear system of equations stemming from discontinuous Galerkin discretizations of second-order elliptic partial differential equations on polytopic meshes. The preconditioner is based on a coarse space and a non-overlapping partition of the computational domain where local solvers are applied in parallel. In particular, the coarse space can potentially be chosen to be non-embedded with respect to the finer space; indeed it can be obtained from the fine grid by employing agglomeration and edge coarsening techniques. We investigate the dependence of the condition number of the preconditioned system with respect to the diffusion coefficient and the discretization parameters, i.e., the mesh size and the polynomial degree of the fine and coarse spaces. Numerical examples are presented which confirm the theoretical bounds

U.S. - MEXICO SUGAR DISPUTE: IMPACT OF NAFTA ON THE SUGAR MARKET

A side agreement to the North American Free Trade Agreement (NAFTA) enables Mexico to ship more duty-free sugar to the United States than under the pre-1994 restrictive country-specific, tariff-rate quota (TRQ) policy. But U.S. and Mexican negotiators disagree over the issue of exactly how much sugar Mexico can actually export to the U.S. under the NAFTA side agreement. Disagreement focuses on which version of the NAFTA side agreement governs this issue. The U.S. argues that a 1993 side letter limits Mexican sugar exports to the U.S. to 250,000 MT. In contrast, Mexico insists it is entitled to ship all of its surplus sugar, currently 600,000 MT, to U.S. Consequently, Mexico has asked for a dispute-settlement panel to resolve the question under NAFTA. Three TRQ liberalization scenarios were simulated to show the possible policy implications. The simulation results report that, due to the sugar TRQ liberalization with Mexico, the net U.S. social welfare increases but U.S. producers lose.International Relations/Trade,

An hr-adaptive discontinuous Galerkin method for advection-diffusion problems

We propose an adaptive mesh refinement strategy based on exploiting a combination of a pre-processing mesh re-distribution algorithm employing a harmonic mapping technique, and standard (isotropic) mesh subdivision for discontinuous Galerkin approximations of advection-diffusion problems. Numerical experiments indicate that the resulting adaptive strategy can efficiently reduce the computed discretization error by clustering the nodes in the computational mesh where the analytical solution undergoes rapid variation

U.S.-MEXICO SUGAR DISPUTE: IMPACT OF NAFTA ON THE SUGAR MARKET

A side agreement to the North American Free Trade Agreement (NAFTA) enables Mexico to ship more duty-free sugar to the United States than under the pre-1994 restrictive country-specific, tariff-rate quota (TRQ) policy. But U.S. and Mexican negotiators disagree over the issue of exactly how much sugar Mexico can actually export to the U.S. under the NAFTA side agreement. Disagreement focuses on which version of the NAFTA side agreement governs this issue. The U.S. argues that a 1993 side letter limits Mexican sugar exports to the U.S. to 250,000 MT. In contrast, Mexico insists it is entitled to ship all of its surplus sugar, currently 600,000 MT, to U.S. Consequently, Mexico has asked for a dispute-settlement panel to resolve the question under NAFTA. Three TRQ liberalization scenarios were simulated to show the possible policy implications. The simulation results report that, due to the sugar TRQ liberalization with Mexico, the net U.S. social welfare increases but U.S. producers lose.International Relations/Trade,

A Limnological Study of Ricks Pond and the Gulpha Creek Drainage in Garland County, Arkansas

A limnological investigation of Ricks Pond and the Gulpha Creek drainage of Garland County, Arkansas was conducted between 1 June 1978, and 21 August 1978. Water samples taken from ten stations on three different dates indicated that the stream and pond systems were typical in water quality characteristics of other small, high gradient streams and impoundments in the Ouachita Mountains of Arkansas. In Ricks Pond, thermal stratification occurred along with the development of an oxygen deficient zone below a depth of one meter. Other water quality parameters indicated that Ricks Pond is a moderately productive ecosystem, with the productivity limited by the nitrogen species. The fecal coliform bacterial counts were very low, indicating no direct input of excessive amounts of fecal matter into the system during the present study. However, a Hot Springs city sewer line runs through the pond, and two manholes emerge from the pond\u27s surface. The possibility exists that this sewer line could discharge raw sewage into Ricks Pond during periods of high water. A biological investigation was also conducted in the study area, and lists of the phytoplankton, periphyton, higher aquatic vegetation, zooplankton, benthic macroinvertebrates, and fishes are presented. Twenty-seven species of fishes were collected from the Gulpha Creek drainage, and no rare or endangered forms were found. Ricks Pond is best-suited for the establishment of a put- and-take fishery for channel catfish, Ictalurus punctatus. The following recommendations were made for the establishment of such a fishery: (1) Renovation of the pond by draining and deepening it; (2) Removal of the sewer line from the pond; (3) Stocking of catchable size channel catfish at the rate of approximately 300-400 pounds per acre; (4) Periodic monitoring of the water quality

A class of domain decomposition preconditioners for hp-discontinuous Galerkin finite element methods

In this article we address the question of efficiently solving the algebraic linear system of equations arising from the discretization of a symmetric, elliptic boundary value problem using hp-version discontinuous Galerkin finite element methods. In particular, we introduce a class of domain decomposition preconditioners based on the Schwarz framework, and prove bounds on the condition number of the resulting iteration operators. Numerical results confirming the theoretical estimates are also presented