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Mathematical Programming: Series A and B
Direct methods for sparse matrices
Direct methods for sparse matrices
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Computer-aided analysis of mechanical systems
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ACM Transactions on Mathematical Software (TOMS)
On the Solution of Equality Constrained Quadratic Programming Problems Arising in Optimization
SIAM Journal on Scientific Computing
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PODS '84 Proceedings of the 3rd ACM SIGACT-SIGMOD symposium on Principles of database systems
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SIAM Journal on Optimization
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MPC '95 Mathematics of Program Construction
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ACM Transactions on Mathematical Software (TOMS)
Graphs, Networks and Algorithms (Algorithms and Computation in Mathematics)
Graphs, Networks and Algorithms (Algorithms and Computation in Mathematics)
Direct Methods for Sparse Linear Systems (Fundamentals of Algorithms 2)
Direct Methods for Sparse Linear Systems (Fundamentals of Algorithms 2)
Conserving energy and momentum in nonlinear dynamics: A simple implicit time integration scheme
Computers and Structures
Exact corotational shell for finite strains and fracture
Computational Mechanics
An alternative formulation for quasi-static frictional and cohesive contact problems
Computational Mechanics
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This work describes an algorithm and corresponding software for incorporating general nonlinear multiple-point equality constraints in a implicit sparse direct solver. It is shown that direct addressing of sparse matrices is possible in general circumstances, circumventing the traditional linear or binary search for introducing (generalized) constituents to a sparse matrix. Nested and arbitrarily interconnected multiple-point constraints are introduced by processing of multiplicative constituents with a built-in topological ordering of the resulting directed graph. A classification of discretization methods is performed and some re-classified problems are described and solved under this proposed perspective. The dependence relations between solution methods, algorithms and constituents becomes apparent. Fracture algorithms can be naturally casted in this framework. Solutions based on control equations are also directly incorporated as equality constraints. We show that arbitrary constituents can be used as long as the resulting directed graph is acyclic. It is also shown that graph partitions and orderings should be performed in the innermost part of the algorithm, a fact with some peculiar consequences. The core of our implicit code is described, specifically new algorithms for direct access of sparse matrices (by means of the clique structure) and general constituent processing. It is demonstrated that the graph structure of the second derivatives of the equality constraints are cliques (or pseudo-elements) and are naturally included as such. A complete algorithm is presented which allows a complete automation of equality constraints, avoiding the need of pre-sorting. Verification applications in four distinct areas are shown: single and multiple rigid body dynamics, solution control and computational fracture.