The FETI-DP domain decomposition method is extended to address the iterative solution of a class of indefinite problems of the form (K−σM)x = b, and a class of complex problems of the form (K − σM + iσD)x = b, where K, M, and D are three real symmetric positive semi-definite matrices arising from the finite element discretization of either second-order elastodynamic problems or fourth-order pla...

We consider two different aspects of FETI-DP domain decomposition methods [8, 23]. In the first part, we describe an adaptive construction of coarse spaces from local eigenvalue problems for the solution of heterogeneous, e.g., multiscale, problems. This strategy of constructing a coarse space is implemented using a deflation approach. In the second part, we introduce new domain decomposition a...

Advanced High Strength Steels (AHSS) provide a good combination of both strength and formability and are therefore applied extensively in the automotive industry, especially in the crash relevant parts of the vehicle. Dual-phase (DP) steel is an example for such AHSS which is widely employed. The excellent macroscopic behavior of this steel is a result of the inherent micro-heterogeneity and co...

A FETI-DP (dual-primal finite element tearing and interconnecting) formulation for the two-dimensional Stokes problem with mortar methods is considered. Separate sets of unknowns are used for velocity on interfaces, and the mortar constraints are enforced on the velocity unknowns by Lagrange multipliers. Average constraints on edges are further introduced as primal constraints to solve the Stok...

Explosive welding (EXW) has advantages in joining metallurgically incompatible metals due to its high quality and simple process. Successful titanium/steel clad plates fabricated by explosive have been extensively reported recent years. However, no research on the fabrication of explosively welded TA2/15CrNi3MoV effect subsequent heat treatment processes plates. This study aims clarify microstr...

FETI and BDD are two widely used substructuring methods for the solution of large sparse systems of linear algebraic equations arizing from discretization of elliptic boundary value problems. The two most advanced variants of these methods are the FETI-DP and the BDDC methods, whose formulation does not require any information beyond the algebraic system of equations in a substructure form. We ...

Eleven isobaric experimental series simulate the fractional crystallization of a 1150 km deep lunar magma ocean. Crystallization begins at 1850 oC with olivine (to 32 per cent solidified, pcs), followed 1600 by olivine+opx±Cr-spinel 62 1210 cpx+plagioclase±olivine±Ti-spinel 97 pcs) and 1060 quartz+cpx+plagioclase+Ti-spinel, leaving 1.8 wt% residual that crystallizes minor K-feldspar apatite in ...