International Business Machines Corporation

Microsoft Technology Licensing, LLC

Philip Starhill

David J Simons

James Evan Undery

Christopher Stephen Messer

Maksim Lepikhin

Keith Seifert

An input mesh can be decomposed into component meshes that can be independently simplified. A computing device can calculate costs of performing candidate edge collapses for a component mesh. The candidate edge collapses can include boundary edge collapses and interior edge collapses. To simplify a component mesh, the execution of boundary edge collapses and the execution of interior edge collapses are interleaved in an order based on the costs of performing the candidate edge collapses. The position of a vertex resulting from a boundary edge collapse can be calculated independently of the interior of the component mesh. When component meshes are simplified in parallel, a boundary that is common to the component meshes can be simplified identically.

Maintaining consistent boundaries in parallel mesh simplification

Advantageously, embodiments of the invention provide techniques for determining dependency relationships between matrix supernodes by storing a list of dependencies for each supernode in a data structure and augmenting this list as needed when a column is moved from one supernode to another while factorizing a series Aof symmetric matrices. As iterating over all supernodes to determine which supernodes a given supernode depends on at the beginning of each factorization adds significant overhead to the computation, embodiments described above maintains a supernode dependency data structure used for each successive factorization, greatly reducing the overhead of the dependency determination.

Maintaining dependencies among supernodes during repeated matrix factorizations

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Philip Starhill