Scholarlink

<p>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&#xa0;<i>m</i> is the number of subdomains in a cluster in one direction, then the cost of the coarse problem decreases with <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(m^6\)</EquationSource> </InlineEquation>, but the number of iterations increases proportionally to only <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\sqrt{m}\)</EquationSource> </InlineEquation>, extending the parallel scalability by several orders. We illustrate the theoretical results by solving problems discretized by billion of nodal variables.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

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

  • 期刊论文

  • 发表日期：

    2025年11月5日

查看全文
  • Zdeněk Dostál,
  • Tomáš Brzobohatý,
  • Oldřich Vlach,
  • Ondřej Meca,
  • Marie Sadowská

摘要

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 \(m^6\) , but the number of iterations increases proportionally to only \(\sqrt{m}\) , extending the parallel scalability by several orders. We illustrate the theoretical results by solving problems discretized by billion of nodal variables.