Computational strategies for surface fitting using thin plate spline finite element methods

Thin plate spline finite element methods are used to fit a surface to an irregularly scattered dataset [S. Roberts, M. Hegland, and I. Altas. Approximation of a Thin Plate Spline Smoother using Continuous Piecewise Polynomial Functions. SIAM, 1:208--234, 2003]. The computational bottleneck for this algorithm is the solution of large, ill-conditioned systems of linear equations at each step of a generalised cross validation algorithm. Preconditioning techniques are investigated to accelerate the convergence of the solution of these systems using Krylov subspace methods. The preconditioners under consideration are block diagonal, block triangular and constraint preconditioners [M. Benzi, G. H. Golub, and J. Liesen. Numerical solution of saddle point problems. Acta Numer., 14:1--137, 2005]. The effectiveness of each of these preconditioners is examined on a sample dataset taken from a known surface. From our numerical investigation, constraint preconditioners appear to provide improved convergence for this surface fitting problem compared to block preconditioners.

Foldback current control for a DG to achieve Fast Arc Extinction in a distribution network

The distribution network reliability can be increased if distributed generators (DGs) are allowed to operate in both grid-connected and islanded operations when the network has a high DG penetration level. However, the current utility regulations do not allow for the islanded operation. The arc faults are the one of the major issues preventing the islanded operation, since the arc will not extinguish if the DGs are not disconnected. In this paper, the effect of a converter interfaced DG on an arc fault is investigated by considering different control strategies for the converter. The foldback current control characteristic is proposed to a converter interfaced DG to achieve quick arc extinction and self-restoration without disconnecting the DG in the event of an arc fault. The results are validated through PSCAD/EMTDC simulations.

Krylov subspace approximations for the exponential Euler method: Error estimates and the harmonic Ritz approximant

We study Krylov subspace methods for approximating the matrix-function vector product φ(tA)b where φ(z) = [exp(z) - 1]/z. This product arises in the numerical integration of large stiff systems of differential equations by the Exponential Euler Method, where A is the Jacobian matrix of the system. Recently, this method has found application in the simulation of transport phenomena in porous media within mathematical models of wood drying and groundwater flow. We develop an a posteriori upper bound on the Krylov subspace approximation error and provide a new interpretation of a previously published error estimate. This leads to an alternative Krylov approximation to φ(tA)b, the so-called Harmonic Ritz approximant, which we find does not exhibit oscillatory behaviour of the residual error.

Volcanology and petrology of submarine volcanoes of the New Hebrides island arc

The New Hebrides Island Arc, an intra-oceanic island chain in the southwest Pacific, is formed by subduction of the Indo-Australian Plate beneath the Pacific Plate. The southern end of the New Hebrides Island Arc is an ideal location to study the magmatic and tectonic interaction of an emerging island arc as this part of the island chain is less than 3 million years old. A tectonically complex island arc, it exhibits a change in relative subduction rate from ~12cm/yr to 6 cm/yr before transitioning to a left-lateral strike slip zone at its southern end. Two submarine volcanic fields, Gemini-Oscostar and Volsmar, occur at this transition from normal arc subduction to sinistral strike slip movement. Multi-beam bathymetry and dredge samples collected during the 2004 CoTroVE cruise onboard the RV Southern Surveyor help define the relationship between magmatism and tectonics, and the source for these two submarine volcanic fields. Gemini-Oscostar volcanic field (GOVF), dominated by northwest-oriented normal faults, has mature polygenetic stratovolcanoes with evidence for explosive subaqueous eruptions and homogeneous monogenetic scoria cones. Volsmar volcanic field (VVF), located 30 km south of GOVF, exhibits a conjugate set of northwest and eastwest-oriented normal faults, with two polygenetic stratovolcanoes and numerous monogenetic scoria cones. A deep water caldera provides evidence for explosive eruptions at 1500m below sea level in the VVF. Both volcanic fields are dominated by low-K island arc tholeiites and basaltic andesites with calcalkalic andesite and dacite being found only in the GOVF. Geochemical signatures of both volcanic fields continue the along-arc trend of decreasing K2O with both volcanic fields being similar to the New Hebrides central chain lavas. Lavas from both fields display a slight depletion in high field strength elements and heavy rare earth elements, and slight enrichments in large-ion lithophile elements and light rare earth elements with respect to N-MORB mantle. Sr and Nd isotope data correlate with heavy rare earth and high field strength element data to show that both fields are derived from depleted mantle. Pb isotopes define Pacific MORB mantle sources and are consistent with isotopic variation along the New Hebrides Island Arc. Pb isotopes show no evidence for sediment contamination; the subduction component enrichment is therefore a slab-derived enrichment. There is a subtle spatial variation in source chemistry which sees a northerly trend of decreasing enrichment of slab-derived fluids.

Arc voltage behavior in GMAW-P under different drop transfer modes

Purpose: Experimental measurements have been made to investigate meaning of the change in voltage for the pulse gas metal arc welding (GMAW-P) process operating under different drop transfer modes. Design/methodology/approach: Welding experiments with different values of pulsing parameter and simultaneous recording of high speed camera pictures and welding signals (such as current and voltage) were used to identify different drop transfer modes in GMAW-P. The investigation is based on the synchronization of welding signals and high speed camera to study the behaviour of voltage signal under different drop transfer modes. Findings: The results reveal that the welding arc is significantly affected by the molten droplet detachment. In fact, results indicate that sudden increase and drop in voltage just before and after the drop detachment can be used to characterize the voltage behaviour of different drop transfer mode in GMAW-P. Research limitations/implications: The results show that voltage signal carry rich information about different drop transfer occurring in GMAW-P. Hence it’s possible to detect different drop transfer modes. Future work should concentrate on development of filters for detection of different drop transfer modes. Originality/value: Determination of drop transfer mode with GMAW-P is crucial for the appropriate selection of pulse welding parameters. As change in drop transfer mode results in poor weld quality in GMAW-P, so in order to estimate the working parameters and ensure stable GMAW-P understanding the voltage behaviour of different drop transfer modes in GMAW-P will be useful. However, in case of GMAW-P hardly any attempt is made to analyse the behaviour of voltage signal for different drop transfer modes. This paper analyses the voltage signal behaviour of different drop transfer modes for GMAW-P.