Flexible Modellerweiterung und Optimierung von Erdbebensimulationen

Simulations of realistic earthquake scenarios require scalable software and extensive supercomputing resources. With increasing fidelity in simulations, advanced rheological and source models need to be incorporated. I introduce a domain-specific language in order to handle the model flexibility in combination with the high efficiency requirements. The contributions in this thesis enabled the to date largest and longest dynamic rupture simulation of the 2004 Sumatra earthquake.Realistische Erdbebensimulationen benötigen skalierbare Software und beträchtliche Rechenressourcen. Mit zunehmender Genauigkeit der Simulationen müssen fortschrittliche rheologische und Quellmodelle integriert werden. Ich führe eine domänenspezifische Sprache ein, um die Modelflexibilität in Kombination mit den hohen Effizienzanforderungen zu beherrschen. Die Beiträge in dieser Arbeit haben die bisher größte und längste dynamische Bruchsimulation des Sumatra-Erdbebens von 2004 ermöglicht

Inelastic material response in multi-physics earthquake rupture simulations

Dynamic rupture models are able to shed light on earthquake source dynamics where direct observations are rare or non-existent. These multi-physics simulations incorporate earthquake rupture along a fault governed by frictional constitutive laws, which is coupled to seismic wave propagation described by the linear elastic wave equation. To accurately model the earthquake process, numerical models need to include realistic material properties such as the ability of rocks to deform plastically. This dissertation extends the Arbitrary High Order Derivative Discontinuous Galerkin (ADER-DG) framework of the dynamic rupture software SeisSol to account for non-linear off-fault plasticity. The impact of plasticity on rupture dynamics and the emitted seismic wave field is investigated in realistic simulations motivated by past earthquakes on geometrically complex faults. We first present the implementation of off-fault plasticity, which is verified in community benchmark problems and by three-dimensional numerical refinement studies. Motivated by the high efficiency of the implementation, we present a large-scale simulation of earthquake rupture along the segmented fault system of the 1992 Landers earthquake including plasticity. The results indicate that spatio-temporal rupture transfers are altered by plastic energy absorption, correlating with locations of geometrical fault complexity. In a next step, the model of the 1992 Landers earthquake is further extended to account for a new degree of realism among dynamic rupture models by incorporating high-resolution topography, 3D velocity structure, and viscoelastic attenuation in addition to off-fault plasticity. The simulation reproduces a broad range of observations including moment release rate, seismic waveform characteristics, mapped off-fault deformation patterns, and peak ground motions. We find that plasticity reduces the directivity effect and the spatial variability of peak ground velocities in comparison to the purely elastic simulation. In addition to this continental strike-slip earthquake, we investigate the effect of off-fault plasticity on source dynamics and seafloor deformation in a 3D subduction zone model of the 2004 Sumatra-Andaman earthquake. Simulated seafloor displacements are drastically altered by inelastic processes within the entire accretionary wedge, depending on fault- strike and the applied regional stress field, which potentially affects the tsunamigenesis. Finally, since these application scenarios show that rupture dynamics and the occurrence of off-fault plasticity are highly influenced by the assumed initial stresses and fault geometry, we propose a workflow to constrain dynamic rupture initial conditions with plasticity by long-term seismic cycling modelling. The exploited seismo-thermo-mechanical model provides a self-consistent slab geometry as well as initial stress and strength conditions that evolve according to the tectonic stress build-up and the temperature-dependent strength of the rocks. The geomechanically constrained subduction zone model suggests that the accretionary wedge is very close to plastic failure such that the occurrence of plastic strain hampers rupture to the trench, but locally increases the vertical seafloor uplift

Multiscale Modeling and Simulation of Deformation Accumulation in Fault Networks

Strain accumulation and stress release along multiscale geological fault networks are fundamental mechanisms for earthquake and rupture processes in the lithosphere. Due to long periods of seismic quiescence, the scarcity of large earthquakes and incompleteness of paleoseismic, historical and instrumental record, there is a fundamental lack of insight into the multiscale, spatio-temporal nature of earthquake dynamics in fault networks. This thesis constitutes another step towards reliable earthquake prediction and quantitative hazard analysis. Its focus lies on developing a mathematical model for prototypical, layered fault networks on short time scales as well as their efficient numerical simulation. This exposition begins by establishing a fault system consisting of layered bodies with viscoelastic Kelvin-Voigt rheology and non-intersecting faults featuring rate-and-state friction as proposed by Dieterich and Ruina. The individual bodies are assumed to experience small viscoelastic deformations, but possibly large relative tangential displacements. Thereafter, semi-discretization in time with the classical Newmark scheme of the variational formulation yields a sequence of continuous, nonsmooth, coupled, spatial minimization problems for the velocities and states in each time step, that are decoupled by means of a fixed point iteration. Subsequently, spatial discretization is based on linear and piecewise constant finite elements for the rate and state problems, respectively. A dual mortar discretization of the non-penetration constraints entails a hierarchical decomposition of the discrete solution space, that enables the localization of the non-penetration condition. Exploiting the resulting structure, an algebraic representation of the parametrized rate problem can be solved efficiently using a variant of the Truncated Nonsmooth Newton Multigrid (TNNMG) method. It is globally convergent due to nonlinear, block Gauß–Seidel type smoothing and employs nonsmooth Newton and multigrid ideas to enhance robustness and efficiency of the overall method. A key step in the TNNMG algorithm is the efficient computation of a correction obtained from a linearized, inexact Newton step. The second part addresses the numerical homogenization of elliptic variational problems featuring fractal interface networks, that are structurally similar to the ones arising in the linearized correction step of the TNNMG method. Contrary to the previous setting, this model incorporates the full spatial complexity of geological fault networks in terms of truly multiscale fractal interface geometries. Here, the construction of projections from a fractal function space to finite element spaces with suitable approximation and stability properties constitutes the main contribution of this thesis. The existence of these projections enables the application of well-known approaches to numerical homogenization, such as localized orthogonal decomposition (LOD) for the construction of multiscale discretizations with optimal a priori error estimates or subspace correction methods, that lead to algebraic solvers with mesh- and scale-independent convergence rates. Finally, numerical experiments with a single fault and the layered multiscale fault system illustrate the properties of the mathematical model as well as the efficiency, reliability and scale-independence of the suggested algebraic solver

Large-Scale Simulations of Complex Turbulent Flows: Modulation of Turbulent Boundary Layer Separation and Optimization of Discontinuous Galerkin Methods for Next-Generation HPC Platforms

The separation of spatially evolving turbulent boundary layer flow near regions of adverse pressure gradients has been the subject of numerous studies in the context of flow control. Although many studies have demonstrated the efficacy of passive flow control devices, such as vortex generators (VGs), in reducing the size of the separated region, the interactions between the salient flow structures produced by the VG and those of the separated flow are not fully understood. Here, wall-resolved large-eddy simulation of a model problem of flow over a backward-facing ramp is studied with a submerged, wall-mounted cube being used as a canonical VG. In particular, the turbulent transport that results in the modulation of the separated flow over the ramp is investigated by varying the size, location of the VG, and the spanwise spacing between multiple VGs, which in turn are expected to modify the interactions between the VG-induced flow structures and those of the separated region. The horseshoe vortices produced by the cube entrain the freestream turbulent flow towards the plane of symmetry. These localized regions of high vorticity correspond to turbulent kinetic energy production regions, which effectively transfer energy from the freestream to the near-wall regions. Numerical simulations indicate that: (i) the gradients and the fluctuations, scale with the size of the cube and thus lead to more effective modulation for large cubes, (ii) for a given cube height the different upstream cube positions affect the behavior of the horseshoe vortex---when placed too close to the leading edge, the horseshoe vortex is not sufficiently strong to affect the large-scale structures of the separated region, and when placed too far, the dispersed core of the streamwise vortex is unable to modulate the flow over the ramp, (iii) if the spanwise spacing between neighboring VGs is too small, the counter-rotating vortices are not sufficiently strong to affect the large-scale structures of the separated region, and if the spacing is too large, the flow modulation is similar to that of an isolated VG. Turbulent boundary layer flows are inherently multiscale, and numerical simulations of such systems often require high spatial and temporal resolution to capture the unsteady flow dynamics accurately. While the innovations in computer hardware and distributed computing have enabled advances in the modeling of such large-scale systems, computations of many practical problems of interest are infeasible, even on the largest supercomputers. The need for high accuracy and the evolving heterogeneous architecture of the next-generation high-performance computing centers has impelled interest in the development of high-order methods. While the new class of recovery-assisted discontinuous Galerkin (RADG) methods can provide arbitrary high-orders of accuracy, the large number of degrees of freedom increases costs associated with the arithmetic operations performed and the amount of data transferred on-node. The purpose of the second part of this thesis is to explore optimization strategies to improve the parallel efficiency of RADG. A cache data-tiling strategy is investigated for polynomial orders 1 through 6, which enhances the arithmetic intensity of RADG to make better utilization of on-node floating-point capability. In addition, a power-aware compute framework is suggested by analyzing the power-performance trade-offs when changing from double to single-precision floating-point types---energy savings of 5 W per node are observed---which suggests that a transprecision framework will likely offer better power-performance balance on modern HPC platforms.PHDMechanical EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/163206/1/suyashtn_1.pd