Ivan Georgiev

Bridging onshore and offshore present‐day kinematics of central and eastern Mediterranean: Implications for crustal dynamics and mantle flow

We present a new kinematic and strain model of an area encompassing the Calabrian and Hellenic subduction zones, western Anatolia and the Balkans. Using Haines and Holts (1993) method, we derive continuous velocity and strain rate fields by interpolating geodetic velocities, including recent GPS data in the Balkans. Relative motion between stable Eurasia and the western Aegean Sea is gradually accommodated by distributed N-S extension from Southern Balkans to the Eastern Corinth Gulf, so that the westward propagation of the North Anatolian Fault (NAF) throughout continental Greece or Peloponnesus is not required. We thus propose that the NAF terminates in north Aegean and that N-S extension localized in the Corinth Gulf and distributed in Southern Balkans is due to the retreat of the Hellenic slab. The motion of the Hyblean plateau, Apulia Peninsula, south Adriatic Sea, Ionian Basin and Sirte plain can be minimized by a single rigid rotation around a pole located in the Sirte plain, compatible with the opening the Pelagian rifts (2–2.5 mm/yr) and seismotectonics in Libya. We interpret the trenchward ultraslow motion of the Calabrian arc (2–2.5 mm/yr) as pure collapse, the Calabrian subduction being now inactive. In the absolute plate motion reference frame, our modeled velocity field depicts two toroidal crustal patterns located at both ends of the Hellenic subduction zone, clockwise in NW Greece and counter-clockwise in western Anatolia. We suggest the NW Greece toroidal pattern is the surface expression of a slab tear and consequent toroidal asthenospheric flow.

Crystallization kinetics and network rigidity

Kinetics of crystal growth in non-isochemical systems is considered taking into account the changes in composition of the residual melt during the process. This leads to the formation of concentration gradients in the vicinity of the new phase. If a component acting as a network modifier is enriched in the crystalline phase, the melt at the interface is enriched in network formers and the glass network will turn from floppy to rigid. Consequently, the crystal grows until a critical concentration is reached, at which the melt locally turns to a rigid one. There is a critical size of the crystal, above which the growth rate strongly decreases because the network former concentration at the interface drops below the threshold limit. The problem is solved numerically and finite differences are used for space and time discretization.

Multilevel preconditioning of rotated bilinear non-conforming FEM problems

Preconditioners based on various multilevel extensions of two-level finite element methods (FEM) lead to iterative methods which often have an optimal order computational complexity with respect to the number of degrees of freedom of the system. Such methods were first presented in [O. Axelsson, P.S. Vassilevski, Algebraic multilevel preconditioning methods I, Numer. Math. 56 (1989) 157-177; O. Axelsson, P.S. Vassilevski, Algebraic multilevel preconditioning methods II, SIAM J. Numer. Anal. 27 (1990) 1569-1590] on (recursive) two-level splittings of the finite element space. The key role in the derivation of optimal convergence rate estimates is played by the constant @c in the so-called strengthened Cauchy-Bunyakowski-Schwarz (CBS) inequality, associated with the angle between the two subspaces of the splitting. More precisely, the value of the upper bound for @c@?(0,1) is a part of the construction of various multilevel extensions of the related two-level methods. In this paper algebraic two-level and multilevel preconditioning algorithms for second-order elliptic boundary value problems are constructed, where the discretization is done using Rannacher-Turek non-conforming rotated bilinear finite elements on quadrilaterals. An important point to make is that in this case the finite element spaces corresponding to two successive levels of mesh refinement are not nested in general. To handle this, a proper two-level basis is required to enable us to fit the general framework for the construction of two-level preconditioners for conforming finite elements and to generalize the method to the multilevel case. The proposed variants of the hierarchical two-level basis are first introduced in a rather general setting. Then, the parameters involved are studied and optimized. The major contribution of the paper is the derived estimates of the constant @c in the strengthened CBS inequality which is shown to allow the efficient multilevel extension of the related two-level preconditioners. Representative numerical tests well illustrate the optimal complexity of the resulting iterative solver.

Multilevel algorithms for Rannacher–Turek finite element approximation of 3D elliptic problems

AbstractGeneralizing the approach of a previous work of the authors, dealing with two-dimensional (2D) problems, we present multilevel preconditioners for three-dimensional (3D) elliptic problems discretized by a family of Rannacher Turek non-conforming finite elements. Preconditioners based on various multilevel extensions of two-level finite element methods (FEM) lead to iterative methods which often have an optimal order computational complexity with respect to the number of degrees of freedom of the system. Such methods were first presented by Axelsson and Vassilevski in the late-1980s, and are based on (recursive) two-level splittings of the finite element space. An important point to make is that in the case of non-conforming elements the finite element spaces corresponding to two successive levels of mesh refinement are not nested in general. To handle this, a proper two-level basis is required to enable us to fit the general framework for the construction of two-level preconditioners for conforming finite elements and to generalize the method to the multilevel case. In the present paper new estimates of the constant γ in the strengthened Cauchy–Bunyakowski–Schwarz (CBS) inequality are derived that allow an efficient multilevel extension of the related two-level preconditioners. Representative numerical tests well illustrate the optimal complexity of the resulting iterative solver, also for the case of non-smooth coefficients. The second important achievement concerns the experimental study of AMLI solvers applied to the case of micro finite element (μFEM) simulation. Here the coefficient jumps are resolved on the finest mesh only and therefore the classical CBS inequality based convergence theory is not directly applicable. The obtained results, however, demonstrate the efficiency of the proposed algorithms in this case also, as is illustrated by an example of microstructure analysis of bones.

Multilevel preconditioning of crouzeix-raviart 3d pure displacement elasticity problems

In this study we demonstrate how some different techniques which were introduced and studied in previous works by the authors can be integrated and extended in the construction of efficient algebraic multilevel iteration methods for more complex problems We devise an optimal order algorithm for solving linear systems obtained from locking-free discretization of 3D pure displacement elasticity problems The presented numerical results illustrate the robustness of the method for nearly incompressible materials.

Supervised 2-Phase Segmentation of Porous Media with Known Porosity

Porous media segmentation is a nontrivial and often quite inaccurate process, due to the highly irregular structure of the segmentation phases and the huge interaction among them. In this paper we perform a 2-class segmentation of a gray-scale 3D image under the restriction that the number of voxels within the phases are a priori fixed. Two parallel algorithms, based on the graph 2-Laplacian model [1] are proposed, implemented, and numerically tested.

Analysis of the CBS constant for quadratic finite elements

We study the behavior of the CBS constant as a quality measure for hierarchical two-level splittings of quadratic FEM stiffness matrices. The article is written in the spirit of [3] where the focus is on the robustness with respect to mesh and coefficient anisotropy. The considered splittings are: Differences and Aggregates (DA); First Reduce (FR); and hierarchical P-decomposition (P). The presented results show sufficient conditions for the existence of optimal order Algebraic Multi-Level Iteration (AMLI) preconditioners.

A computational approach for remediation procedures in horizontal subsurface flow constructed wetlands

A large-scale computational approach for groundwater flow and contaminant transport and removal in porous media is presented. Emphasis is given to remediation procedures in horizontal subsurface flow constructed wetlands. For the numerical procedure, the MODFLOW computer code family is used. Application is made for the simulation of horizontal subsurface flow wetlands pilot-scale units, constructed and operated in Democritus University of Thrace, Xanthi, Greece. The effects of the inlet and outlet recharge positions to the optimum contaminant removal are also numerically investigated.

Tall RC Buildings Environmentally Degradated and Strengthened by Cables Under Multiple Earthquakes: A Numerical Approach

A numerical investigation is presented for the seismic analysis of tall reinforced concrete (RC) Civil Engineering structures, which have been degradated due to extreme environmental actions and are strengthened by cable elements. The effects of multiple earthquakes on such RC building frames are computed. Damage indices are estimated in order to compare the seismic response of the structures before and after the retrofit by cable element strengthening, and so to elect the optimum strengthening version.

Multilevel preconditioning of 2D Rannacher-Turek FE problems: additive and multiplicative methods

In the present paper we concentrate on algebraic two-level and multilevel preconditioners for symmetric positive definite problems arising from discretization by Rannacher-Turek non-conforming rotated bilinear finite elements on quadrilaterals. An important point to make is that in this case the finite element spaces corresponding to two successive levels of mesh refinement are not nested (in general). To handle this, a proper two-level basis is required in order to fit the general framework for the construction of two-level preconditioners for conforming finite elements and to generalize the methods to the multilevel case. The proposed variants of hierarchical two-level basis are first introduced in a rather general setting. Then, the involved parameters are studied and optimized. As will be shown, the obtained bounds - in particular - give rise to optimal order AMLI methods of additive type. The presented numerical tests fully confirm the theoretical estimates.