An Approach to Improve the Smoothing Process Based on Non-uniform Redistribution

PACLIC 19 / Taipei, taiwan / December 1-3, 200

A discontinuous Galerkin moving mesh method for Hamilton-Jacobi equations

In this paper we consider the numerical solution of first-order Hamilton-Jacobi equations using the combination of a discontinuous Galerkin finite element method and an adaptive $r$-refinement (mesh movement) strategy. Particular attention is given to the choice of an appropriate adaptivity criterion when the solution becomes discontinuous. Numerical examples in one and two dimensions are presented to demonstrate the effectiveness of the adaptive procedure

A moving mesh method with variable relaxation time

We propose a moving mesh adaptive approach for solving time-dependent partial differential equations. The motion of spatial grid points is governed by a moving mesh PDE (MMPDE) in which a mesh relaxation time \tau is employed as a regularization parameter. Previously reported results on MMPDEs have invariably employed a constant value of the parameter \tau. We extend this standard approach by incorporating a variable relaxation time that is calculated adaptively alongside the solution in order to regularize the mesh appropriately throughout a computation. We focus on singular problems involving self-similar blow-up to demonstrate the advantages of using a variable relaxation ime over a fixed one in terms of accuracy, stability and efficiency.Comment: 21 page

Investigating optimal cutting configurations for the contour method of weld residual stress measurement

The present work examines optimal cutting configurations for the measurement of weld residual stresses (WRS) using the contour method. The accuracy of a conventional, single-cut configuration that employs rigid clamping is compared with novel, double-embedded cutting configurations that rely on specimen self-constraint during cutting. Numerical analyses examine the redistribution of WRS and the development of cutting-induced plasticity (CIP) in a three-pass austenitic slot weld (NeT TG4) during the cutting procedure for each configuration. Stress intensity factor (SIF) analyses are first used as a screening tool; these analyses characterise lower stress intensities near the cutting surface when double-embedded cutting configurations are used, relative to SIF profiles from a single-cut process. The lower stress intensities indicate the development of CIP – which will ultimately affect back-calculated WRS – is less likely to occur when using an embedded configuration. The improvements observed for embedded cutting approaches are confirmed using three-dimensional finite element (FE) cutting simulations. The simulations reveal significant localised plasticity that forms in the material ligaments located between the pilot holes and the outer edges of the specimen. This plasticity is caused by WRS redistribution during the cutting process. The compressive plasticity in these material ligaments is shown to reduce the overall tensile WRS near the weld region before this region is sectioned, thereby significantly reducing the amount of CIP when cutting through the weld region at a later stage of the cutting procedure. Further improvements to the embedded cutting configuration are observed when the equilibrating compressive stresses in material ligaments are removed entirely (via sectioning) prior to sectioning of the high WRS region in the vicinity of the weld. All numerical results are validated against a series of WRS measurements performed using the contour method on a set of NeT TG4 benchmark weld specimens

Estimating Local Function Complexity via Mixture of Gaussian Processes

Real world data often exhibit inhomogeneity, e.g., the noise level, the sampling distribution or the complexity of the target function may change over the input space. In this paper, we try to isolate local function complexity in a practical, robust way. This is achieved by first estimating the locally optimal kernel bandwidth as a functional relationship. Specifically, we propose Spatially Adaptive Bandwidth Estimation in Regression (SABER), which employs the mixture of experts consisting of multinomial kernel logistic regression as a gate and Gaussian process regression models as experts. Using the locally optimal kernel bandwidths, we deduce an estimate to the local function complexity by drawing parallels to the theory of locally linear smoothing. We demonstrate the usefulness of local function complexity for model interpretation and active learning in quantum chemistry experiments and fluid dynamics simulations.Comment: 19 pages, 16 figure