The All-floating BETI Method: Numerical Results

Abstract

Summary. The all-floating BETI method considers all subdomains as floating subdomains and improves the overall asymptotic complexity of the BETI method. This effect and the scalability of the method are shown in numerical examples.

Robust FETI Solvers for Multiscale Elliptic PDEs

“…However, the flux density |B| may vary strongly along subdomain boundaries and large values of |B| appear mostly at singularities of the potential u, e. g., near material corners. Contrary to the usual suggestion to choose subdomain partitions that resolve material interfaces in order to obtain robustness (for numerical examples see [4,5]), our new bounds (7), (9) suggest that it might be more advantageous to put each peak of |B| and thus each material corner into the center of a subdomain. Fig.…”

All-floating coupled data-sparse boundary and interface-concentrated finite element tearing and interconnecting methods

“…Following [10] (see also [36]) and taking the all-floating idea into account [26,27] (see also [7] for a closely related approach called total FETI), we tear the global skeleton potential vector u C on all subdomain boundaries Γ i including the Dirichlet parts by introducing the individual local unknowns u C,i = R i u C . The global continuity of the potentials on Γ i \ Γ and the Dirichlet boundary conditions on Γ D = Γ are now enforced by the constraints…”

“…, p, where the coefficient a(•) is slightly varying, we use the upper bounds a i for the entries in Q. The matrix L 0 is defined by the representation of λ in the form λ = L 0 λ 0 + λ e (27) with known λ e = QG(G QG) −1 e fulfilling the constraints G λ e = e, and unknown L 0 λ 0 ∈ ker G , i. e., G L 0 λ 0 = 0. The right-hand side of BETI-FETI-2 system (24) is defined by the relations d C,i = b C,i − B C,i λ e for i = 1, .…”

The all-floating boundary element tearing and interconnecting method

“…In [14,20], we suggested the "all-floating" BETI method. Related numerical results were presented in [21]. In the meantime, the all-floating formulation was also applied for the coupling of FETI and BETI methods [15,25].…”