When solving numerically the stiff second order ODE system obtained after semidiscretizing the wave-type partial differential equation (PDE) with the finite element method (FEM), and similarly to the HHTα method, which allows the numerical damping of the undesirable high frequency modes associated to FEM semidiscretization, we have constructed a modification of the 2-order BDF method (the BDF2 ...

The classical techniques for determining weights in finite difference formulas were either computationally slow or very limited in their scope (e.g., specialized recursions for centered and staggered approximations, for Adams–Bashforth-, Adams–Moulton-, and BDF-formulas for ODEs, etc.). Two recent algorithms overcome these problems. For equispaced grids, such weights can be found very convenien...

We develope a difference calculus analogous to the differential geometry by translating the forms and exterior derivatives to similar expressions with difference operators, and apply the results to fields theory on the lattice [Ref. 1]. Our approach has the advantage with respect to other attempts [Ref. 2-6] that the Lorentz invariance is automatically preserved as it can be seen explicitely in...

The numerical treatment of linear-quadratic regulator problems on finite time horizons for parabolic partial differential equations requires the solution of large-scale differential Riccati equations (DREs). Typically the coefficient matrices of the resulting DRE have a given structure (e.g. sparse, symmetric or low rank). Here we discuss numerical methods for solving DREs capable of exploiting...

We investigate the long time behavior of the following efficient second order in time scheme for the 2D Navier-Stokes equation in a periodic box: 3ω − 4ω + ω 2k +∇(2ψ − ψ) · ∇(2ω − ω)− ν∆ω = f, −∆ψ = ω. The scheme is a combination of a 2nd order in time backward-differentiation (BDF) and a special explicit Adams-Bashforth treatment of the advection term. Therefore only a linear constant coeffic...

This paper presents a novel Bayesian Discriminating Features (BDF) method for multiple frontal face detection. The BDF method, which is trained on images from only one database, yet works on test images from diverse sources, displays robust generalization performance. The novelty of this paper comes from the integration of the discriminating feature analysis of the input image, the statistical ...

The dynamic dataflow (DDF) domain in Ptolemy is a superset of the synchronous dataflow (SDF) and Boolean dataflow (BDF) domains. In the SDF domain, a star consumes and produces a fixed number of particles per invocation (or “firing”). This static information (the number of particles produced or consumed for each star) makes possible compile-time scheduling. In the BDF domain, some actors with d...

Abstract: Transient analysis is an important circuit simulation technique. The circuit model, which is a system of differential-algebraic equations, is solved for a given initial condition using numerical time integration techniques. Multirate methods are efficient if the dynamical behaviour of the circuit model is not uniform. This paper deals with the analysis and control of the discretizatio...

Two di erent time-stepping schemes are investigated for a phaseeld model of solidi cation of a pure material. A rst order accurate semiexplicit scheme which is computationally cheap per time step is compared to a more accurate fully implicit BDF-discretization. The implementation of fast Poisson and Newton-GMRES solvers are discussed in some detail. Convergence rates are experimentally validate...

This study introduces, analyses and implements space-time discretizations of two-dimensional active dissipative partial differential equations such as the Topper–Kawahara equation; this is the two-dimensional extension of the dispersively modified Kuramoto–Sivashinsky equation found in falling film hydrodynamics. The spatially periodic initial value problem is considered as the size of the peri...