Level set based multi-scale methods for large deformation contact problems
We consider the numerical simulation of contact problems in elasticity with large deformations. The non-penetration condition is described by means of a signed distance function to the obstacle's boundary. Techniques from level set methods allow for an appropriate numerical approximation of the...
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| Vydáno v: | Applied numerical mathematics Ročník 61; číslo 4; s. 428 - 442 |
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| Jazyk: | angličtina |
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Elsevier B.V
01.04.2011
Elsevier |
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| ISSN: | 0168-9274, 1873-5460 |
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| Abstract | We consider the numerical simulation of contact problems in elasticity with large deformations. The non-penetration condition is described by means of a signed distance function to the obstacle's boundary. Techniques from level set methods allow for an appropriate numerical approximation of the signed distance function preserving its non-smooth character. The emerging non-convex optimization problem subject to non-smooth inequality constraints is solved by a non-smooth multiscale SQP method in combination with a non-smooth multigrid method as interior solver. Several examples in three space dimensions including applications in biomechanics illustrate the capability of our methods. |
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| AbstractList | We consider the numerical simulation of contact problems in elasticity with large deformations. The non-penetration condition is described by means of a signed distance function to the obstacle's boundary. Techniques from level set methods allow for an appropriate numerical approximation of the signed distance function preserving its non-smooth character. The emerging non-convex optimization problem subject to non-smooth inequality constraints is solved by a non-smooth multiscale SQP method in combination with a non-smooth multigrid method as interior solver. Several examples in three space dimensions including applications in biomechanics illustrate the capability of our methods. |
| Author | Krause, Rolf Mohr, Christina |
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| Cites_doi | 10.1006/jcph.1994.1155 10.1007/s007910050003 10.1137/S1052623401383558 10.1137/070682514 10.1016/0021-9991(87)90031-3 10.1002/nme.466 10.1137/S106482759732455X 10.1002/nme.568 10.1137/08071819X 10.1002/nla.374 10.1007/3-540-31761-9_2 10.1007/s007910100052 10.1016/0045-7825(90)90098-7 10.1002/nme.264 10.1016/j.cma.2004.08.006 10.1098/rspa.1972.0026 10.1073/pnas.93.4.1591 |
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| Keywords | Contact problems Non-linear elasticity Level set methods Multigrid methods Non-smooth optimization Large deformations Three-dimensional calculations Level set Optimization method Mechanical contact Numerical approximation Numerical analysis Linear elasticity Applied mathematics Multiscale method Inequality constraint Smooth function Variational calculus Numerical simulation Mathematical programming |
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| SubjectTerms | Approximation Boundaries Calculus of variations and optimal control Contact Contact problems Deformation Exact sciences and technology Large deformations Level set methods Mathematical analysis Mathematical models Mathematics Multigrid methods Multiscale methods Non-linear elasticity Non-smooth optimization Numerical analysis Numerical analysis. Scientific computation Numerical approximation Numerical methods in mathematical programming, optimization and calculus of variations Numerical methods in optimization and calculus of variations Sciences and techniques of general use Solvers |
| Title | Level set based multi-scale methods for large deformation contact problems |
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