In this paper, we propose a piecewise linear decision tree and its generalized form, namely the (G)PWL-DT, which introduces linearity overcomes discontinuity of existing constant trees (PWC-DT). The proposed (G)PWL-DT inherits basic topology interpretability by recursively partitioning domain into subregions, are represented leaf nodes. Rather than indicator function, employs rectifier units (R...

We consider the fast solution of large, piecewise smooth minimization problems as typically arising from the nite element discretization of porous media ow. For lack of smoothness, usual Newton multigrid methods cannot be applied. We propose a new approach based on a combination of convex minization with constrained Newton linearization. No regularization is involved. We show global convergence...

A new redistancing method for piecewise polynomial finite element level set functions is introduced. The method directly computes the distance to the implicitly given discrete level set. Rigorous error bounds and numerical experiments are provided. Both show that, up to constants, the method is as good as the nodal interpolation of the computationally unavailable signed distance function of the...

Preconditioning of Discontinuous Galerkin Methods for Second Order Elliptic Problems. (December 2007) Veselin Asenov Dobrev, B.S., Sofia University Chair of Advisory Committee: Dr. Raytcho Lazarov We consider algorithms for preconditioning of two discontinuous Galerkin (DG) methods for second order elliptic problems, namely the symmetric interior penalty (SIPG) method and the method of Baumann ...

A trajectory piecewise-linear (TPWL) approach is developed for a computational fluid dynamics (CFD) model of the two-dimensional Euler equations. The approach uses a weighted combination of linearized models to represent the nonlinear CFD system. The proper orthogonal decomposition (POD) is then used to create a reduced-space basis, onto which the TPWL model is projected. This projection yields...

Computational efficiency of solving the dynamics of highly oscillatory systems is an important issue due to the requirement of small step size of explicit numerical integration algorithms. A system is considered to have an oscillatory solution if it contains a fast solution that varies regularly about a slow solution. This paper investigates the use of the so-called Local Linearization Method (...

A numerical approach is presented for an inequality problem arising in the earthquake analysis of adjacent buildings. This problem concerns the unilateral contact-impact between neighboring buildings, when friction and P-delta effects are taken into account. The proposed numerical approach is based on a double discretization, in space and time, and on optimization methods. First, the Finite Ele...

In this paper, a rigorous computational method to compute solutions of piecewisesmooth systems using a functional analytic approach based on Chebyshev series is introduced. A general theory, based on the radii polynomial approach, is proposed to compute crossing periodic orbits for continuous and discontinuous (Filippov) piecewise-smooth systems. Explicit analytic estimates to carry the compute...

We consider the problem of fitting a continuous piecewise linear function to a finite set of data points, modeled as a mathematical program with convex objective. We review some fitting problems that can be modeled as convex programs, and then introduce mixed-binary generalizations that allow variability in the regions defining the best-fit function’s domain. We also study the additional constr...