Numerical Methods for Multilattices

Among the efficient numerical methods based on atomistic models, the quasicontinuum (QC) method has attracted growing interest in recent years. The QC method was first developed for crystalline materials with Bravais lattice and was later extended to multilattices (Tadmor et al, 1999). Another existing numerical approach to modeling multilattices is homogenization. In the present paper we review the existing numerical methods for multilattices and propose another concurrent macro-to-micro method in the numerical homogenization framework. We give a unified mathematical formulation of the new and the existing methods and show their equivalence. We then consider extensions of the proposed method to time-dependent problems and to random materials.Comment: 31 page

Multiscale Partition of Unity

We introduce a new Partition of Unity Method for the numerical homogenization of elliptic partial differential equations with arbitrarily rough coefficients. We do not restrict to a particular ansatz space or the existence of a finite element mesh. The method modifies a given partition of unity such that optimal convergence is achieved independent of oscillation or discontinuities of the diffusion coefficient. The modification is based on an orthogonal decomposition of the solution space while preserving the partition of unity property. This precomputation involves the solution of independent problems on local subdomains of selectable size. We deduce quantitative error estimates for the method that account for the chosen amount of localization. Numerical experiments illustrate the high approximation properties even for 'cheap' parameter choices.Comment: Proceedings for Seventh International Workshop on Meshfree Methods for Partial Differential Equations, 18 pages, 3 figure

Domains of Archean mantle lithosphere deciphered by seismic anisotropy- initial results from the LAPNET array in northern Fennoscandia

Peer reviewe

Deep-seated lateral velocity variations beneath the GRF array inferred from mislocation patterns and P residuals

The analysis of mislocation patterns and the three-dimensional inversion of travel-time residuals for P waves measured at the GRF array reveal the existence of strong lateral velocity variations beneath the array. The most expressive phenomenon consists of an increase of P-wave velocities in the upper mantle from north to south, in addition to a possible thickening of the lithosphere to the south; especially the Moldanubian part of the Bohemian massif located to the southeast of the GRF array is characterized by high P-wave velocities in the upper mantle. The systematic change of the magnitude of the residual variation across the array, depending on the incidence angle for P waves, leads to the conclusion that a low-velocity zone exists in the upper mantle to the northeast of subarray A. The appearance of low-velocity material in the vicinity of the border between the two tectonic units, namely the Saxothuringian zone to the north and the Moldanubian zone to the south, might be connected to the deep structure of the graben area which extends to the northeast into the Egergraben.           ARK: https://n2t.net/ark:/88439/y046952 Permalink: https://geophysicsjournal.com/article/224 &nbsp

A priori convergence estimates for a rough Poisson-Dirichlet problem with natural vertical boundary conditions

Stents are medical devices designed to modify blood flow in aneurysm sacs, in order to prevent their rupture. Some of them can be considered as a locally periodic rough boundary. In order to approximate blood flow in arteries and vessels of the cardio-vascular system containing stents, we use multi-scale techniques to construct boundary layers and wall laws. Simplifying the flow we turn to consider a 2-dimensional Poisson problem that conserves essential features related to the rough boundary. Then, we investigate convergence of boundary layer approximations and the corresponding wall laws in the case of Neumann type boundary conditions at the inlet and outlet parts of the domain. The difficulty comes from the fact that correctors, for the boundary layers near the rough surface, may introduce error terms on the other portions of the boundary. In order to correct these spurious oscillations, we introduce a vertical boundary layer. Trough a careful study of its behavior, we prove rigorously decay estimates. We then construct complete boundary layers that respect the macroscopic boundary conditions. We also derive error estimates in terms of the roughness size epsilon either for the full boundary layer approximation and for the corresponding averaged wall law.Comment: Dedicated to Professor Giovanni Paolo Galdi 60' Birthda

Domains of Archean mantle lithosphere deciphered by seismic anisotropy – inferences from the LAPNET array in northern Fennoscandia

An international LAPNET array (2007–2009, http://www.oulu.fi/sgo-oty/lapnet) of the POLENET/LAPNET sub-project of the POLENET-IPY consortium, related to seismic and geodetic studies in the Arctic regions, consisted of about 60 broadband seismic stations located on the territory of northern Finland and adjacent parts of Sweden, Norway and Russia. We analyze relative P-wave travel-time deviations evaluated for a subset of 90 teleseismic events recorded by the LAPNET array and show examples of lateral variations of shear-wave splitting to demonstrate variability of fabrics of the Archean mantle lithosphere. The initial results clearly demonstrate the Archean mantle lithosphere consists of domains with consistent fabrics reflecting fossil anisotropic structures. 3-D self-consistent anisotropic models with inclined symmetry axes accommodate two independent sets of body-wave anisotropic observations. Individual domains are delimited by boundaries (sutures), where the anisotropic parameters change. The results obtained from the LAPNET array fill a gap in structural studies of the upper mantle beneath northern Fennoscandia

From mountain summits to roots: Crustal structure of the Eastern Alps and Bohemian Massif along longitude 13.3°E

The crustal structure of the Eastern Alps and adjacent tectonic units investigated in this work sheds new light on the relationship of surface geology to geodynamic processes operating at depth. Of particular interest are the nature of a previously proposed Moho gap south and east of the Tauern Window, the plate tectonic affinity of the steeply dipping Eastern Alpine slab, and the relationship of the Alps to the Neogene sedimentary basins and the Bohemian Massif. To address these questions, we use various seismological approaches based on converted waves from the temporary passive experiment EASI (Eastern Alpine Seismic Investigation), a complementary experiment of the AlpArray project. The EASI is a densely spaced, 540 km long seismic network along 13.3°E we operated for more than a year. The uppermost-crustal structures in and near the Alps exhibit dipping layers and/or tilted anisotropy that correlate well with surface geology observations. The Moho, despite its variable appearance, is clearly identified along most of the swath. The Variscan lithospheric blocks beneath the Bohemian Massif are imaged with sub-vertical boundaries. Beneath the Eastern Alps, the shape of the Moho is consistent with bi-vergent orogenic thickening, with a steeper and deeper-reaching Adriatic plate plunging northwards beneath the European plate in the north. At the junction of these plates at depth, around the previously proposed Moho gap, the root of the Eastern Alps is a broad trough characterized by a zone of low velocity-gradient that is up to 20 km thick, transitioning between crust and mantle. Our receiver-function results corroborate earlier lithosphere-upper mantle seismic tomography images, and highlight the Adriatic affinity of the Eastern Alpine slab. The zigzag deployment pattern of stations in the EASI experiment also allows distinction of short-wavelength variations perpendicular to the profile, both within the shallow and the deep crust. This underlines the importance of applying 3D imaging in complex geodynamic systems.ISSN:0040-195

Mantle lithosphere transition from the East European Craton to the Variscan Bohemian Massif imaged by shear-wave splitting

We analyse splitting of teleseismic shear waves recorded during the PASSEQ passive experiment (2006–2008) focused on the upper mantle structure across and around the Trans-European Suture Zone (TESZ). Altogether 1009 pairs of the delay times of the slow split shear waves and orientations of the polarized fast shear waves exhibit lateral variations across the array, as well as back-azimuth dependences of measurements at individual stations. Variable components of the splitting parameters can be associated with fabrics of the mantle lithosphere of tectonic units. In comparison with a distinct regionalization of the splitting parameters in the Phanerozoic part of Europe that particularly in the Bohemian Massif (BM) correlate with the large-scale tectonics, variations of anisotropic parameters around the TESZ and in the East European Craton (EEC) are smooth and of a transitional character. No general and abrupt change in the splitting parameters (anisotropic structure) can be related to the Teisseyre–Tornquist Zone (TTZ), marking the edge of the Precambrian province on the surface. Instead, regional variations of anisotropic structure were found along the TESZ/TTZ. The coherence of anisotropic signals evaluated beneath the northern part of the Brunovistulian in the eastern rim of the BM and the pattern continuation to the NE towards the TTZ, support the idea of a common origin of the lithosphere micro-plates, most probably related to Baltica. Smooth changes in polarizations of the core-mantle boundary refracted shear waves (SKS), polarizations, or even a large number of null splits northward of the BM and further across the TESZ towards the EEC indicate less coherent fabrics and a transitional character of structural changes in the mantle beneath the surface trace of the TESZ/TTZ. The narrow and near-vertical TTZ in the crust does not seem to have a steep continuation in the mantle lithosphere. The mantle part of the TESZ, whose crust was formed by an assemblage of suspect terranes adjoining the EEC edge from the southwest, appears in our measurements of anisotropy as a relatively broad transitional zone in between the two lithospheric segments of different ages. We suggest a southwestward continuation of the Precambrian mantle lithosphere beneath the TESZ and the adjacent Phanerozoic part of Europe, probably as far as towards the Bohemian Massif.Peer reviewe