Results 1  10
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13
A fast variational framework for accurate solidfluid coupling
 ACM Trans. Graph
, 2007
"... Figure 1: Left: A solid stirring smoke runs at interactive rates, two orders of magnitude faster than previously. Middle: Fully coupled rigid bodies of widely varying density, with flow visualized by marker particles. Right: Interactive manipulation of immersed rigid bodies. Physical simulation has ..."
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Cited by 49 (3 self)
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Figure 1: Left: A solid stirring smoke runs at interactive rates, two orders of magnitude faster than previously. Middle: Fully coupled rigid bodies of widely varying density, with flow visualized by marker particles. Right: Interactive manipulation of immersed rigid bodies. Physical simulation has emerged as a compelling animation technique, yet current approaches to coupling simulations of fluids and solids with irregular boundary geometry are inefficient or cannot handle some relevant scenarios robustly. We propose a new variational approach which allows robust and accurate solution on relatively coarse Cartesian grids, allowing possibly orders of magnitude faster simulation. By rephrasing the classical pressure projection step as a kinetic energy minimization, broadly similar to modern approaches to rigid body contact, we permit a robust coupling between fluid and arbitrary solid simulations that always gives a wellposed symmetric positive semidefinite linear system. We provide several examples of efficient fluidsolid interaction and rigid body coupling with subgrid cell flow. In addition, we extend the framework with a new boundary condition for freesurface flow, allowing fluid to separate naturally from solids.
Staggered Projections for Frictional Contact in Multibody Systems
"... Figure 1: Staggered Projections resolves frictional contact between a wide range of rigid and deformable models at rates suitable for (a) interactive haptic simulations, as well as accurate animations that capture important frictional contact phenomena such as: (b) largedeformation frictional conta ..."
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Cited by 24 (5 self)
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Figure 1: Staggered Projections resolves frictional contact between a wide range of rigid and deformable models at rates suitable for (a) interactive haptic simulations, as well as accurate animations that capture important frictional contact phenomena such as: (b) largedeformation frictional contact with reduced StVK models, (c) largescale, frictional stacking and jamming of large numbers of objects without constraint drift, (d) and long term stable simulation of difficult, frictionally dependent structures. We present a new discrete velocitylevel formulation of frictional contact dynamics that reduces to a pair of coupled projections and introduce a simple fixedpoint property of this coupled system. This allows us to construct a novel algorithm for accurate frictional contact resolution based on a simple staggered sequence of projections. The algorithm accelerates performance using warm starts to leverage the potentially high temporal coherence between contact states and provides users with direct control over frictional accuracy. Applying this algorithm to rigid and deformable systems, we obtain robust and accurate simulations of frictional contact behavior not previously possible, at rates suitable for interactive haptic simulations, as well as largescale animations. By construction, the proposed algorithm guarantees exact, velocitylevel contact constraint enforcement and obtains longterm stable and robust integration. Examples are given to illustrate the performance, plausibility and accuracy of the obtained solutions.
The Semismooth Algorithm for Large Scale Complementarity Problems
, 1999
"... Complementarity solvers are continually being challenged by modelers demanding improved reliability and scalability. Building upon a strong theoretical background, the semismooth algorithm has the potential to meet both of these requirements. We briefly discuss relevant theory associated with th ..."
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Cited by 19 (7 self)
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Complementarity solvers are continually being challenged by modelers demanding improved reliability and scalability. Building upon a strong theoretical background, the semismooth algorithm has the potential to meet both of these requirements. We briefly discuss relevant theory associated with the algorithm and describe a sophisticated implementation in detail. Particular emphasis is given to robust methods for dealing with singularities in the linear system and to large scale issues. Results on the MCPLIB test suite indicate that the code is robust and has the potential to solve very large problems.
Complementarity And Related Problems: A Survey
, 1998
"... This survey gives an introduction to some of the recent developments in the field of complementarity and related problems. After presenting two typical examples and the basic existence and uniqueness results, we focus on some new trends for solving nonlinear complementarity problems. Extensions to ..."
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Cited by 14 (0 self)
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This survey gives an introduction to some of the recent developments in the field of complementarity and related problems. After presenting two typical examples and the basic existence and uniqueness results, we focus on some new trends for solving nonlinear complementarity problems. Extensions to mixed complementarity problems, variational inequalities and mathematical programs with equilibrium constraints are also discussed.
Mathematical Programs with Equilibrium Constraints: Automatic Reformulation and Solution via Constrained Optimization
, 2002
"... Constrained optimization has been extensively used to... This paper briefly reviews some methods available to solve these problems and describes a new suite of tools for working with MPEC models. Computational results demonstrating... ..."
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Cited by 13 (3 self)
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Constrained optimization has been extensively used to... This paper briefly reviews some methods available to solve these problems and describes a new suite of tools for working with MPEC models. Computational results demonstrating...
Limit Analysis of Frictional Block Assemblies as a Mathematical Program With Complementarity Constraints
, 1999
"... The computation of the collapse loads of discrete rigid block systems, characterized by frictional (nonassociative) and tensionless contact interfaces, is formulated and solved as a special constrained optimization problem known as a Mathematical Program with Equilibrium Constraints (MPEC). In the p ..."
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Cited by 6 (2 self)
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The computation of the collapse loads of discrete rigid block systems, characterized by frictional (nonassociative) and tensionless contact interfaces, is formulated and solved as a special constrained optimization problem known as a Mathematical Program with Equilibrium Constraints (MPEC). In the present instance, some of the essential constraints are defined by a complementarity system involving the orthogonality of two signconstrained vectors. Due to its intrinsic complexity, MPECs are computationally very hard to solve. In this paper, we investigate a simple numerical scheme, involving appropriate relaxation of the complementarity term, to solve this nonstandard limit analysis problem. Some computational results are presented to illustrate potentialities of the method. Keywords: Limit analysis, friction, mathematical programming. 1 Introduction The analysis of masonry structures has been the subject of a rich literature spanning over the last few hundred years, as indicated by He...
Preprocessing Complementarity Problems
, 2001
"... Preprocessing techniques are extensively used by the linear and integer programming communities as a means to improve model formulation by reducing size and complexity. Adaptations and extensions of these methods for use within the complementarity framework are detailed. The preprocessor developed i ..."
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Cited by 3 (2 self)
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Preprocessing techniques are extensively used by the linear and integer programming communities as a means to improve model formulation by reducing size and complexity. Adaptations and extensions of these methods for use within the complementarity framework are detailed. The preprocessor developed is comprised of two phases. The rst recasts a complementarity problem as a variational inequality over a polyhedral set and exploits the uncovered structure to x variables and remove constraints. The second discovers information about the function and utilizes complementarity theory to eliminate variables. The methodology is successfully employed to preprocess several models. Keywords: mixed complementarity, preprocessing 1. INTRODUCTION General purpose codes for solving complementarity problems have previously lacked one signicant feature: a powerful preprocessor. The benets of preprocessing have long been known to the linear [1, 2] and integer [19] programming communities, yet have no...
Case Studies in Complementarity: Improving Model Formulation
 Ill{Posed Variational Problems and Regularization Techniques, number 477 in Lecture Notes in Economics and Mathematical Systems
, 1998
"... Over the past several years, many practitioners have been formulating nonlinear variational inequalities as mixed complementarity problems within modeling languages such as GAMS and AMPL. Sometimes the models generated are poorly specified, either because the function is undefined near the solut ..."
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Cited by 3 (2 self)
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Over the past several years, many practitioners have been formulating nonlinear variational inequalities as mixed complementarity problems within modeling languages such as GAMS and AMPL. Sometimes the models generated are poorly specified, either because the function is undefined near the solution or the problem is illconditioned or singular. In this paper, we look at information provided by the PATH solver about the model that can be used to identify problem areas and improve formulation. Descriptions and uses of the data provided are detailed via several case studies. 1 Introduction Developing a practical model of a complex situation is a difficult task in which an approximate representation is initially constructed and then iteratively refined until an accurate formulation is obtained. During the intermediate stages, the models generated have a tendency to be illdefined, illconditioned, and/or singular. Information generated by a solver can help the modeler to detect t...
Formulating and Solving Nonlinear Programs as Mixed Complementarity Problems
 Optimization. Lecture Notes in Economics and Mathematical Systems
, 2000
"... . We consider a primaldual approach to solve nonlinear programming problems within the AMPL modeling language, via a mixed complementarity formulation. The modeling language supplies the first order and second order derivative information of the Lagrangian function of the nonlinear problem using au ..."
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Cited by 3 (0 self)
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. We consider a primaldual approach to solve nonlinear programming problems within the AMPL modeling language, via a mixed complementarity formulation. The modeling language supplies the first order and second order derivative information of the Lagrangian function of the nonlinear problem using automatic differentiation. The PATH solver finds the solution of the first order conditions which are generated automatically from this derivative information. In addition, the link incorporates the objective function into a new merit function for the PATH solver to improve the capability of the complementarity algorithm for finding optimal solutions of the nonlinear program. We test the new solver on various test suites from the literature and compare with other available nonlinear programming solvers. Keywords: Complementarity problems, nonlinear programs, automatic differentiation, modeling languages. 1 Introduction While the use of the simplex algorithm for linear programs in the 1940's h...
EXTENDING MODELING SYSTEMS: STRUCTURE AND SOLUTION
"... Keywords Some extensions of a modeling system are described that facilitate higher level structure identification within a model. These structures, which often involve complementarity relationships, can be exploited by modern large scale mathematical programming algorithms. A specific implementation ..."
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Keywords Some extensions of a modeling system are described that facilitate higher level structure identification within a model. These structures, which often involve complementarity relationships, can be exploited by modern large scale mathematical programming algorithms. A specific implementation of an extended mathematical programming tool is outlined that communicates structure in a computationally beneficial manner from the GAMS modeling system to an appropriate solver. Modeling, complementarity, nonlinear programming, variational inequalities