Numerical investigation of the conditioning for plane wave discontinuous Galerkin methods

We present a numerical study to investigate the conditioning of the plane wave discontinuous Galerkin discretization of the Helmholtz problem. We provide empirical evidence that the spectral condition number of the plane wave basis on a single element depends algebraically on the mesh size and the wave number, and exponentially on the number of plane wave directions; we also test its dependence on the element shape. We show that the conditioning of the global system can be improved by orthogonalization of the local basis functions with the modified Gram-Schmidt algorithm, which results in significantly fewer GMRES iterations for solving the discrete problem iteratively.Comment: Submitted as a conference proceeding; minor revisio

GeNN: a code generation framework for accelerated brain simulations

Large-scale numerical simulations of detailed brain circuit models are important for identifying hypotheses on brain functions and testing their consistency and plausibility. An ongoing challenge for simulating realistic models is, however, computational speed. In this paper, we present the GeNN (GPU-enhanced Neuronal Networks) framework, which aims to facilitate the use of graphics accelerators for computational models of large-scale neuronal networks to address this challenge. GeNN is an open source library that generates code to accelerate the execution of network simulations on NVIDIA GPUs, through a flexible and extensible interface, which does not require in-depth technical knowledge from the users. We present performance benchmarks showing that 200-fold speedup compared to a single core of a CPU can be achieved for a network of one million conductance based Hodgkin-Huxley neurons but that for other models the speedup can differ. GeNN is available for Linux, Mac OS X and Windows platforms. The source code, user manual, tutorials, Wiki, in-depth example projects and all other related information can be found on the project website http://genn-team.github.io/genn/

CFD investigation of a complete floating offshore wind turbine

This chapter presents numerical computations for floating offshore wind turbines for a machine of 10-MW rated power. The rotors were computed using the Helicopter Multi-Block flow solver of the University of Glasgow that solves the Navier-Stokes equations in integral form using the arbitrary Lagrangian-Eulerian formulation for time-dependent domains with moving boundaries. Hydrodynamic loads on the support platform were computed using the Smoothed Particle Hydrodynamics method. This method is mesh-free, and represents the fluid by a set of discrete particles. The motion of the floating offshore wind turbine is computed using a Multi-Body Dynamic Model of rigid bodies and frictionless joints. Mooring cables are modelled as a set of springs and dampers. All solvers were validated separately before coupling, and the loosely coupled algorithm used is described in detail alongside the obtained results

A global method for coupling transport with chemistry in heterogeneous porous media

Modeling reactive transport in porous media, using a local chemical equilibrium assumption, leads to a system of advection-diffusion PDE's coupled with algebraic equations. When solving this coupled system, the algebraic equations have to be solved at each grid point for each chemical species and at each time step. This leads to a coupled non-linear system. In this paper a global solution approach that enables to keep the software codes for transport and chemistry distinct is proposed. The method applies the Newton-Krylov framework to the formulation for reactive transport used in operator splitting. The method is formulated in terms of total mobile and total fixed concentrations and uses the chemical solver as a black box, as it only requires that on be able to solve chemical equilibrium problems (and compute derivatives), without having to know the solution method. An additional advantage of the Newton-Krylov method is that the Jacobian is only needed as an operator in a Jacobian matrix times vector product. The proposed method is tested on the MoMaS reactive transport benchmark.Comment: Computational Geosciences (2009) http://www.springerlink.com/content/933p55085742m203/?p=db14bb8c399b49979ba8389a3cae1b0f&pi=1

An inexact dual logarithmic barrier method for solving sparse semidefinite programs

A dual logarithmic barrier method for solving large, sparse semidefinite programs is proposed in this paper. The method avoids any explicit use of the primal variable X and therefore is well-suited to problems with a sparse dual matrix S. It relies on inexact Newton steps in dual space which are computed by the conjugate gradient method applied to the Schur complement of the reduced KKT system. The method may take advantage of low-rank representations of matrices Ai to perform implicit matrix-vector products with the Schur complement matrix and to compute only specific parts of this matrix. This allows the construction of the partial Cholesky factorization of the Schur complement matrix which serves as a good preconditioner for it and permits the method to be run in a matrix-free scheme. Convergence properties of the method are studied and a polynomial complexity result is extended to the case when inexact Newton steps are employed. A Matlab-based implementation is developed and preliminary computational results of applying the method to maximum cut and matrix completion problems are reported

PKA and Epac cooperate to augment bradykinin-induced interleukin-8 release from human airway smooth muscle cells

Background: Airway smooth muscle contributes to the pathogenesis of pulmonary diseases by secreting inflammatory mediators such as interleukin-8 (IL-8). IL-8 production is in part regulated via activation of G(q)-and G(s)-coupled receptors. Here we study the role of the cyclic AMP (cAMP) effectors protein kinase A (PKA) and exchange proteins directly activated by cAMP (Epac1 and Epac2) in the bradykinin-induced IL-8 release from a human airway smooth muscle cell line and the underlying molecular mechanisms of this response.Methods: IL-8 release was assessed via ELISA under basal condition and after stimulation with bradykinin alone or in combination with fenoterol, the Epac activators 8-pCPT-2'-O-Me-cAMP and Sp-8-pCPT-2'-O-Me-cAMPS, the PKA activator 6-Bnz-cAMP and the cGMP analog 8-pCPT-2'-O-Me-cGMP. Where indicated, cells were pre-incubated with the pharmacological inhibitors Clostridium difficile toxin B-1470 (GTPases), U0126 (extracellular signal-regulated kinases ERK1/2) and Rp-8-CPT-cAMPS (PKA). The specificity of the cyclic nucleotide analogs was confirmed by measuring phosphorylation of the PKA substrate vasodilator-stimulated phosphoprotein. GTP-loading of Rap1 and Rap2 was evaluated via pull-down technique. Expression of Rap1, Rap2, Epac1 and Epac2 was assessed via western blot. Downregulation of Epac protein expression was achieved by siRNA. Unpaired or paired two-tailed Student's t test was used.Results: The beta(2)-agonist fenoterol augmented release of IL-8 by bradykinin. The PKA activator 6-Bnz-cAMP and the Epac activator 8-pCPT-2'-O-Me-cAMP significantly increased bradykinin-induced IL-8 release. The hydrolysis-resistant Epac activator Sp-8-pCPT-2'-O-Me-cAMPS mimicked the effects of 8-pCPT-2'-O-Me-cAMP, whereas the negative control 8-pCPT-2'-O-Me-cGMP did not. Fenoterol, forskolin and 6-Bnz-cAMP induced VASP phosphorylation, which was diminished by the PKA inhibitor Rp-8-CPT-cAMPS. 6-Bnz-cAMP and 8-pCPT-2'-O-Me-cAMP induced GTP-loading of Rap1, but not of Rap2. Treatment of the cells with toxin B-1470 and U0126 significantly reduced bradykinin-induced IL-8 release alone or in combination with the activators of PKA and Epac. Interestingly, inhibition of PKA by Rp-8-CPT-cAMPS and silencing of Epac1 and Epac2 expression by specific siRNAs largely decreased activation of Rap1 and the augmentation of bradykinin-induced IL-8 release by both PKA and Epac.Conclusion: Collectively, our data suggest that PKA, Epac1 and Epac2 act in concert to modulate inflammatory properties of airway smooth muscle via signaling to the Ras-like GTPase Rap1 and to ERK1/2.</p