Reducing sparse nonlinear eigenproblems by automated multi-level substructuring
Advances in Engineering Software
An Implementation and Evaluation of the AMLS Method for Sparse Eigenvalue Problems
ACM Transactions on Mathematical Software (TOMS)
Finite Elements in Analysis and Design
The Lanczos Method for Parameterized Symmetric Linear Systems with Multiple Right-Hand Sides
SIAM Journal on Matrix Analysis and Applications
Theoretical relations between domain decomposition and dynamic substructuring
PARA'04 Proceedings of the 7th international conference on Applied Parallel Computing: state of the Art in Scientific Computing
Elemental: A New Framework for Distributed Memory Dense Matrix Computations
ACM Transactions on Mathematical Software (TOMS)
Improving eigenpairs of automated multilevel substructuring with subspace iterations
Computers and Structures
Exploiting domain knowledge to optimize parallel computational mechanics codes
Proceedings of the 27th international ACM conference on International conference on supercomputing
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We present an automated multilevel substructuring (AMLS) method for eigenvalue computations in linear elastodynamics in a variational and algebraic setting. AMLS first recursively partitions the domain of the PDE into a hierarchy of subdomains. Then AMLS recursively generates a subspace for approximating the eigenvectors associated with the smallest eigenvalues by computing partial eigensolutions associated with the subdomains and the interfaces between them. We remark that although we present AMLS for linear elastodynamics, our formulation is abstract and applies to generic H1-elliptic bilinear forms.In the variational formulation, we define an interface mass operator that is consistent with the treatment of elastic properties by the familiar Steklov--Poincaré operator. With this interface mass operator, all of the subdomain and interface eigenvalue problems in AMLS become orthogonal projections of the global eigenvalue problem onto a hierarchy of subspaces. Convergence of AMLS is determined in the continuous setting by the truncation of these eigenspaces, independent of other discretization schemes.The goal of AMLS, in the algebraic setting, is to achieve a high level of dimensional reduction, locally and inexpensively, while balancing the errors associated with truncation and the finite element discretization. This is accomplished by matching the mesh-independent AMLS truncation error with the finite element discretization error. Our report ends with numerical experiments that demonstrate the effectiveness of AMLS on a model problem and an industrial problem.