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Associate Professor, Department of Mathematics, Texas A&M University

Over the past 20 years, there have been two landmark shifts in computational science and engineering The transition from sequential to parallel computing, and the emergence of very large libraries that provide a huge amount of functionality to application programs in much the same way as MATLAB does for many tasks that can be written in the language of linear algebra. Unfortunately, while the codes written in many applications areas are well parallelized today, they have only recently started to be based on existing libraries.

In this webinar, I will explore what led to these libraries, what they offer, and how they can help communities write codes that are far better, faster, and less complex, yet utilizing far more complex algorithms, that are smaller, better tested, and better documented. Our software, the open source library deal.II (see www.dealii.org), is used as an example to exemplify these benefits and its application to geodynamics. While this talk will focus on deal.II as the underlying library, the following talk in this webinar series, by Timo Heister, will focus on an application built on deal.II, the mantle convection code ASPECT.

Texas A&M University

We present the new open source code ASPECT for modeling convection in the earth's mantle (see www.dealii.org/aspect). ASPECT uses modern numerical methods and provides very good parallel scalability; this is achieved by building on the open source finite element library deal.II (seewww.dealii.org and the previous webinar talk by Wolfgang Bangerth).

In this webinar, talk we will step through the many ingredients necessary for a modern simulation code: time discretization, nonlinear methods, linear solvers, stabilization, adaptivity, and parallelization. Finally, the effectiveness is shown in several numerical examples.

Argonne National Laboratory

This presentation will introduce the leading methodologies for large-scale linear and nonlinear solvers, guidelines for algorithmic scalability and parallel performance, and adaptation of these methods to problems in geodynamics. Software support will be discussed and accessible numerical examples will be provided.

Nanyang Technological University

The Relax software implements a semi analytic solver in the Fourier domain to simulation stress change and deformation in the lithosphere caused by earthquakes and other environmental changes. Recently, Rousset et al. (2012) used Relax to simulate coupled afterslip and viscoelastic flow following the 1999 Chi-Chi earthquake. In the webinar, we will explore how to use Relax to simulate Coulomb stress change, afterslip, and 3D viscoelastic model of postseismic deformation. We will learn how to setup the input files, and visualize the simulation. We will generate maps of surface displacement and stress with GMT and explore large data sets in 3D using Paraview. Through examples, we will see how Relax can be used for education and research. And most important of all: Relax!

US Geological Survey

This seminar will provide an introduction to Bayesian analysis and its advantages and disadvantages relative to traditional optimization approaches for solving geophysical inverse problems. Bayesian methods have particular value for solving ill-posed inverse problems for two reasons. First, under-determined inverse problems by definition have more than one solution. The solution to the Bayesian inverse problem is the probability density function which describes the ensemble of all possible models which are consistent with the observed data and any constraints imposed on the model. This is a much more informative solution than computing one solution to the inverse problem via traditional optimization. Second, Bayesian inverse solutions may be obtained without evaluating the inverse of the design matrix, so that no matter how ill-posed the inverse problem is, regularization is never required (although it can be used if desired).

Demonstrations of how to apply Bayesian methods to real geophysical problems will be given. Although these examples will be drawn primarily from earthquake source modeling, the methods and tools presented are completely generic and applicable to a wide array of geophysical inverse problems, and the discussion will be broadly directed to the modeling community. Two end-member Bayesian approaches will be discussed. One is the completely generalized approach in which any desired cost function and a priori constraints can be used to fit the data. In practice, this often requires that the solution be computed via Monte Carlo simulation, which can have extreme computational expense for large numbers of free parameters. (Monte Carlo sampling strategies will be discussed as well.) The second approach is to choose the cost function and prior constraints carefully so as to obtain an analytical solution to the inverse problem. The cost of computing the solution becomes trivial but, depending on the physical system being modeled, some compromise in the inversion design may be required to keep the solution analytical. *Please note that the first 15 sec has no audio due to recording errors.*

CU Boulder

This webinar will begin with a brief overview of recent efforts to model convection and dynamos in the Sun and other stars. Such models (massive stars in particular) share many fundamental aspects in common with geodynamo models. Until recently, stellar dynamo studies that employed pseudospectral methods involving spherical harmonics also faced the same fundamental challenge as geodynamo models; scalability. After describing how this obstacle has been overcome within the last year for the Anelastic Spherical Harmonic code, I will present the essential elements of a scalable pseudo-spectral framework (based on MPI) that CIG is now assembling into a community dynamo model. I will conclude with some thoughts on how this framework may be extended to incorporate GPUs and/or a hybrid OpenMP/MPI approach.

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