We consider the solution of a second order elliptic PDE with inhomogeneous Dirichlet data by means of adaptive lowest-order FEM. As is usually done in practice, the given Dirichlet data are discretized by nodal interpolation. As model example serves the Poisson equation with mixed Dirichlet-Neumann boundary conditions. For error estimation, we use an edge-based residual error estimator which re...

In the paper we report on a second stage of our efforts towards a library design for the solution of very large set of linear equations arising from the finite difference approximation of elliptic partial differential equations (PDE). Particularly a family of Krylov subspace iterative based methods (in the paper exemplified by the archetypical Krylov space method Conjugate Gradient method) are ...

Proper generalised decompositions (PGDs) are a family of methods for efficiently solving high-dimensional PDEs. Convergence of PGD algorithms can be proven provided that the weak form of the PDE can be recast as the minimisation of some energy functional. A large number of elliptic problems, such as the Stokes problem, cannot be guaranteed to converge when employing a Galerkin PGD. Least-square...

Optimization problems with constraints which require the solution of a partial differential equation arise widely in many areas of the sciences and engineering, in particular in problems of design. The solution of such PDEconstrained optimization problems is usually a major computational task. Here we consider simple problems of this type: distributed control problems in which the 2and 3-dimens...

Exposure of perfused rat lungs to lipopolysaccharides (LPS) causes induction of cyclooxygenase-2 followed by thromboxane (TX)-mediated bronchoconstriction (BC). Recently, phosphodiesterase (PDE) inhibitors have received much interest because they not only are bronchodilators but also can suppress release of proinflammatory mediators. In the present study, we investigated the effect of three dif...

The rod photoreceptor phosphodiesterase (PDE) is unique among all known vertebrate PDE families for several reasons. It is a catalytic heterodimer (alphabeta); it is directly activated by a G-protein, transducin; and its active sites are regulated by inhibitory gamma subunits. Rod PDE binds cGMP at two noncatalytic sites on the alphabeta dimer, but their function is unclear. We show that transd...

Recent studies have demonstrated that functionally discrete pools of phosphodiesterase (PDE) activity regulate distinct cellular functions. While the importance of localized pools of enzyme activity has become apparent, few studies have estimated enzyme activity within discrete subcellular compartments. Here we present an approach to estimate near-membrane PDE activity. First, total PDE activit...

The binding of cGMP to the noncatalytic sites on two isoforms of the phosphodiesterase (PDE) from mammalian rod outer segments has been characterized to evaluate their role in regulating PDE during phototransduction. Nonactivated, membrane-associated PDE (PDE-M, alpha beta gamma2) has one exchangeable site for cGMP binding; endogenous cGMP remains nonexchangeable at the second site. Non-activat...

In addition to its emerging immunodulatory properties, theophylline is a bronchodilator and also decreases mean pulmonary arterial pressure in vivo. The mechanism of action of this drug remains controversial; adenosine antagonism, phosphodiesterase (PDE) inhibition and other actions have been advanced to explain its effectiveness in asthma. Cyclic adenosine monophosphate (AMP) and cyclic guanos...