Using a detailed multilevel analysis of the complete hp-Multigrid as Smoother algorithm accurate predictions are obtained of the spectral radius and operator norms of the multigrid error transformation operator. This multilevel analysis is used to optimize the coefficients in the semi-implicit Runge-Kutta smoother, such that the spectral radius of the multigrid error transformation operator is ...

Displacement finite element models of various beam theories have been developed traditionally using conventional finite element basis functions (i.e., cubic Hermite, equi-spaced Lagrange interpolation functions, or spectral/hp Legendre functions). Various finite element models of beams differ from each other in the choice of the interpolation functions used for the transverse deflection w, tota...

A new improved ”Simple complete proofs of the Serre spectral sequence theorems”. In ([B]) I set forth a proof of the Serre calculation of E and claimed among other things that unlike my previous attempts to prove this in graduate course lectures, this proof was routine. On presenting this material in class, I discovered it was not as routine as I had imagined. With the help of Pallavi Jayawart ...

We report on a high-fidelity, spectral/hp element algorithm developed for the direct numerical simulation of thermal convection problems. consider incompressible Navier–Stokes (NS) and advection–diffusion equations coupled through body-forcing term. The flow is driven by prescribed flowrate forcing with explicit treatment nonlinear advection terms. body-force term also decouples both NS equatio...

In physiological conditions, heart period (HP) affects systolic arterial pressure (SAP) through diastolic runoff and Starling's law, but, the reverse relation also holds as a result of the continuous action of baroreflex control. The prevailing mechanism sets the dominant temporal direction in the HP-SAP interactions (i.e., causality). We exploited cross-conditional entropy to assess HP-SAP cau...

The hierarchical reconstruction (HR) [Liu, Shu, Tadmor and Zhang, SINUM ’07] has been successfully applied to prevent oscillations in solutions computed by finite volume, Runge-Kutta discontinuous Galerkin, spectral volume schemes for solving hyperbolic conservation laws. In this paper, we demonstrate that HR can also be combined with spectral/hp element method for solving hyperbolic conservati...