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Hybrid TFETI domain decomposition for solving huge 3D multibody contact problems.

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Title: Hybrid TFETI domain decomposition for solving huge 3D multibody contact problems.
Authors: Dostál, Zdeněk1,2 (AUTHOR) zdenek.dostal@vsb.cz, Brzobohatý, Tomáš1 (AUTHOR) tomas.brzobohaty@vsb.cz, Vlach, Oldřich1,2 (AUTHOR) oldrich.vlach@vsb.cz, Meca, Ondřej1 (AUTHOR) ondrej.meca@vsb.cz, Sadowská, Marie2 (AUTHOR) marie.sadowska@vsb.cz
Source: Computational Mechanics. May2026, Vol. 77 Issue 5, p1405-1418. 14p.
Subjects: Domain decomposition methods, Contact mechanics, Parallel algorithms, Numerical calculations, Quadratic programming, Lagrange multiplier
Abstract: We adopt the three-level hybrid domain decomposition TFETI method for solving 3D multibody frictionless contact problems. We decompose the bodies into subdomains, then partly interconnect the subdomains into clusters by the rigid body modes of the interiors of adjacent faces, and finally generate constraints enforcing the classical boundary and contact conditions. After switching to the discretized dual problem, we get the quadratic programming problem in Lagrange multipliers with bound and equality constraints and a well-conditioned Hessian that specialized solvers can solve with asymptotically linear complexity. If m is the number of subdomains in a cluster in one direction, then the cost of the coarse problem decreases with , but the number of iterations increases proportionally to only , extending the parallel scalability by several orders. We illustrate the theoretical results by solving problems discretized by billion of nodal variables. [ABSTRACT FROM AUTHOR]
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Database: Engineering Source
Description
Abstract:We adopt the three-level hybrid domain decomposition TFETI method for solving 3D multibody frictionless contact problems. We decompose the bodies into subdomains, then partly interconnect the subdomains into clusters by the rigid body modes of the interiors of adjacent faces, and finally generate constraints enforcing the classical boundary and contact conditions. After switching to the discretized dual problem, we get the quadratic programming problem in Lagrange multipliers with bound and equality constraints and a well-conditioned Hessian that specialized solvers can solve with asymptotically linear complexity. If m is the number of subdomains in a cluster in one direction, then the cost of the coarse problem decreases with , but the number of iterations increases proportionally to only , extending the parallel scalability by several orders. We illustrate the theoretical results by solving problems discretized by billion of nodal variables. [ABSTRACT FROM AUTHOR]
ISSN:01787675
DOI:10.1007/s00466-025-02712-3