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

Batch solution of small PDEs with the OPS DSL

In this paper we discuss the challenges and optimisations opportunities when solving a large number of small, equally sized discretised PDEs on regular grids. We present an extension of the OPS (Oxford Parallel library for Structured meshes) embedded Domain Specific Language, and show how support can be added for solving multiple systems, and how OPS makes it easy to deploy a variety of transformations and optimisations. The new capabilities in OPS allow to automatically apply data structure transformations, as well as execution schedule transformations to deliver high performance on a variety of hardware platforms. We evaluate our work on an industrially representative finance simulation on Intel CPUs, as well as NVIDIA GPUs

An explicit hybridizable discontinuous Galerkin method for the 3D time-domain Maxwell equations

International audienceWe present an explicit hybridizable discontinuous Galerkin (HDG) method for numerically solving the system of three-dimensional (3D) time-domain Maxwell equations. The method is fully explicit similarly to classical so-called DGTD (Dis-continuous Galerkin Time-Domain) methods, is also high-order accurate in both space and time and can be seen as a generalization of the classical DGTD scheme based on upwind fluxes. We provide numerical results aiming at assessing its numerical convergence properties by considering a model problem and we present preliminary results of the superconvergence property on the H curl norm

Expression of LIM kinase 1 is associated with reversible G1/S phase arrest, chromosomal instability and prostate cancer

<p>Abstract</p> <p>Background</p> <p>LIM kinase 1 (LIMK1), a LIM domain containing serine/threonine kinase, modulates actin dynamics through inactivation of the actin depolymerizing protein cofilin. Recent studies have indicated an important role of LIMK1 in growth and invasion of prostate and breast cancer cells; however, the molecular mechanism whereby LIMK1 induces tumor progression is unknown. In this study, we investigated the effects of ectopic expression of LIMK1 on cellular morphology, cell cycle progression and expression profile of LIMK1 in prostate tumors.</p> <p>Results</p> <p>Ectopic expression of LIMK1 in benign prostatic hyperplasia cells (BPH), which naturally express low levels of LIMK1, resulted in appearance of abnormal mitotic spindles, multiple centrosomes and smaller chromosomal masses. Furthermore, a transient G1/S phase arrest and delayed G2/M progression was observed in BPH cells expressing LIMK1. When treated with chemotherapeutic agent Taxol, no metaphase arrest was noted in these cells. We have also noted increased nuclear staining of LIMK1 in tumors with higher Gleason Scores and incidence of metastasis.</p> <p>Conclusion</p> <p>Our results show that increased expression of LIMK1 results in chromosomal abnormalities, aberrant cell cycle progression and alteration of normal cellular response to microtubule stabilizing agent Taxol; and that LIMK1 expression may be associated with cancerous phenotype of the prostate.</p

Neural Dynamics during Anoxia and the “Wave of Death”

Recent experiments in rats have shown the occurrence of a high amplitude slow brain wave in the EEG approximately 1 minute after decapitation, with a duration of 5–15 s (van Rijn et al, PLoS One 6, e16514, 2011) that was presumed to signify the death of brain neurons. We present a computational model of a single neuron and its intra- and extracellular ion concentrations, which shows the physiological mechanism for this observation. The wave is caused by membrane potential oscillations, that occur after the cessation of activity of the sodium-potassium pumps has lead to an excess of extracellular potassium. These oscillations can be described by the Hodgkin-Huxley equations for the sodium and potassium channels, and result in a sudden change in mean membrane voltage. In combination with a high-pass filter, this sudden depolarization leads to a wave in the EEG. We discuss that this process is not necessarily irreversible

Neuroregeneration in neurodegenerative disorders

<p>Abstract</p> <p>Background</p> <p>Neuroregeneration is a relatively recent concept that includes neurogenesis, neuroplasticity, and neurorestoration - implantation of viable cells as a therapeutical approach.</p> <p>Discussion</p> <p>Neurogenesis and neuroplasticity are impaired in brains of patients suffering from Alzheimer's Disease or Parkinson's Disease and correlate with low endogenous protection, as a result of a diminished growth factors expression. However, we hypothesize that the brain possesses, at least in early and medium stages of disease, a "neuroregenerative reserve", that could be exploited by growth factors or stem cells-neurorestoration therapies.</p> <p>Summary</p> <p>In this paper we review the current data regarding all three aspects of neuroregeneration in Alzheimer's Disease and Parkinson's Disease.</p

Locally Implicit Discontinuous Galerkin Methods for Time-Domain Maxwell's Equations

International audienceAn attractive feature of discontinuous Galerkin (DG) spatial discretization is the possibility of using locally refined space grids to handle geometrical details. However, when combined with an explicit integration method to numerically solve a time-dependent partial differential equation, this readily leads to unduly large step size restrictions caused by the smallest grid elements. If the local refinement is strongly localized such that the ratio of fine to coarse elements is small, the unduly step size restrictions can be overcome by blending an implicit and an explicit scheme where only solution variables living at fine elements are implicitly treated. The counterpart of this approach is having to solve a linear system per time step. But due to the assumed small fine to coarse elements ratio, the overhead will also be small while the solution can be advanced in time with step sizes determined by the coarse elements. We propose to present two locally implicit methods for the time-domain Maxwell's equations. Our purpose is to compare the two with DG spatial discretization so that the most efficient one can be advocated for future use. Finally we will present a preliminary numerical investigation to increase the order of convergence