In this chapter, we propose a stable and efficient algorithm for animating cloth-like materials using mass-spring systems. An integration scheme derived from implicit integration allows us to obtain interactive realistic animation of any mass-spring network. We alleviate the need to solve a linear system through the use of a predictor-corrector approach: We first compute a rapid approximation o...

[Received 8 May 1987 and in revised form 23 May 1988] In this paper the two-dimensional flow of fresh and salt water through a homogeneous aquifer is considered. The two fluids are assumed to be separated by a sharp interface. They differ only in their specific weight. This difference induces a flow in the aquifer which in turn causes a motion of the interface. We present a mathematical formula...

We propose primal-dual path-following Mehrotra-type predictor-corrector methods for solving convex quadratic semidefinite programming (QSDP) problems of the form: minX{2X • Q(X) + C • X : A(X) = b,X 0}, where Q is a self-adjoint positive semidefinite linear operator on Sn, b ∈ Rm, and A is a linear map from Sn to Rm. At each interior-point iteration, the search direction is computed from a dens...

We propose a family of search directions based on primal-dual entropy in the contextof interior-point methods for linear optimization. We show that by using entropy based searchdirections in the predictor step of a predictor-corrector algorithm together with a homogeneousself-dual embedding, we can achieve the current best iteration complexity bound for linear opti-mization. The...

It is still difficult for traditional methods to simulate fluid-structure interaction (FSI) problems which are increasingly used to model cardiovascular system, and human organism. This contribution develops a new numerical method to analyze FSI, based on smoothed particle hydrodynamics (SPH). The Lagrangian and meshless characteristics of SPH presents distinct features to devise the method by ...

In this work a new optimized symmetric eight-step embedded predictor-corrector method (EPCM) with minimal phase-lag and algebraic order ten is presented. The method is based on the symmetric multistep method of Quinlan-Tremaine [1], with eight steps and eighth algebraic order and is constructed to solve numerically IVPs with oscillatory solutions. We compare the new method to some recently cons...

A-priori individual interconnect length estimates can be used to make placement efficient and reduce delay and power consumption in a circuit. However, finding lengths of individual interconnects before their terminals have been placed can be a daunting task. In this thesis, the main characteristics that need to be considered while designing an individual a-priori length estimation technique fo...

Two predictor-corrector methods of order m = Ω(logn) are proposed for solving sufficient linear complementarity problems. The methods produce a sequence of iterates in the N− ∞ neighborhood of the central path. The first method requires an explicit upper bound κ of the handicap of the problem while the second method does not. Both methods have O((1 + κ)1+1/m √ nL) iteration complexity. They are...

It has been shown in various papers that most interior-point algorithms and their analysis can be generalized to semidefinite optimization. This paper presents an extension of the recent variant of Mehrotra’s predictor-corrector algorithm that was proposed by Salahi et al. (2005) for linear optimization problems. Based on the NT (Nesterov and Todd 1997) direction as Newton search direction it i...

Three primal-dual interior-point algorithms for homogeneous cone programming are presented. They are a short-step algorithm, a large-update algorithm, and a predictor-corrector algorithm. These algorithms are described and analyzed based on a characterization of homogeneous cone via T -algebra. The analysis show that the algorithms have polynomial iteration complexity.