# Confirmed Speakers

- Susanne Brenner, Louisiana State University
*Additive Schwarz Theory* - Xiao-Chuan Cai, University of Colorado at Boulder,
*Domain Decomposition: From Poisson to Coupled Multi-physics Problems* - Juan Calvo, University of Costa Rica
*A virtual coarse space for two-level overlapping Schwarz methods* - Raymond Chan, Chinese University of Hong Kong,
*Point-spread function reconstruction in ground-based astronomy* - Clark Dohrmann, Sandia National Laboratories
*On the Design and Analysis of Coarse Spaces for Domain Decomposition Methods* - Hyea Hyun Kim, Kyung Hee University, Korea,
*Adaptive BDDC and FETI-DP algorithms* - Axel Klawonn, University of Cologne
*FETI-DP and BDDC for Composite Materials - Adaptive Coarse Spaces in 3D* - Duk-Soon Oh, Rutgers University
*Multigrid methods for H(div) with nonoverlapping domain decomposition smoothers* - Luca Pavarino, University of Pavia,
*Scalable Domain Decomposition Preconditioners for cardiac electro-mechanical simulations* - Oliver Rheinbach, TU Bergakademie Freiberg
*Domain Decomposition for Extreme Scale Computing* - Marcus Sarkis, Worcester Polytechnic Institute
*Robust Discretizations based on Adaptive Selection of Primal Constraints* - Simone Scacchi, University of Milan,
*BDDC preconditioners for isogeometric analysis* -
Barry Smith, Argonne National Laboratory,
*Composability in algebraic solvers and ODE integrators***(canceled)** - Nicole Spillane, Ecole Polytechnique,
*Adaptive Multipreconditioning for Symmetric and Non-Symmetric Problems* - Daniel Szyld, Temple University,
*Asynchronous Optimized Schwarz, Theory and Experiments* - Xuemin Tu, University of Kansas
*BDDC domain decomposition for hybrid discontinuous Galerkin Methods* - Barbara Wohlmuth, TU Munich
*Domain decomposition meets multigrid* - Jinchao Xu, Pennsylvania State University
*Overlapping Schwarz Methods with Randomized Ordering* - Stefano Zampini, KAUST
*On the robustness and prospects of BDDC and FETI-DP methods for finite element discretizations of elliptic PDEs*

### Abstracts

**Speaker:** Susanne Brenner, Louisiana State University

**Title:** Additive Schwarz Theory

**Abstract:**

The theory for additive Schwarz methods, introduced by Dryja and Widlund circa
1987, has been a major driving force behind the development of domain
decomposition methods in the last thirty years. In this talk I will give an
account of this theory from a personal perspective.

**Speaker:** Xiao-Chuan Cai, University of Colorado at Boulder

**Title:** Domain Decomposition: From Poisson to Coupled Multi-physics Problems

**Abstract:**

In 1987, Dryja and Widlund introduced a domain decomposition method "Additive
Schwarz Method" (ASM) and showed that it works well for the Poisson equation.
Over the past 30 years, ASM has evolved into a major algorithm for solving many
types of partial differential equations on large scale parallel computers with
millions of cores. In this talk, we discuss some recent development of ASM for
solving multi-physics problems involving fluid-structure interaction with
applications in biomechanics.

**Speaker:** Juan Calvo, University of Costa Rica

**Title:** A virtual coarse space for two-level overlapping Schwarz methods

**Abstract:**

We present a coarse space for irregular subdomains based on virtual elements
for nodal problems in 2D. Its dimension equals the number of subdomain vertices
and results are insensitive to large jumps in the coefficients of the elliptic
problem across the interface. The condition number of the preconditioned system
grows linearly as a function of the relative overlap. Some numerical
experiments that verify the result are shown.

**Speaker:** Raymond Chan, Chinese University of Hong Kong

**Title:** Point-spread function reconstruction in ground-based astronomy

**Abstract:**

Because of atmospheric turbulence, images of objects in outer space acquired
via ground-based telescopes are usually blurry. One way to estimate the
blurring kernel or point spread function (PSF) is to make use of the aberration
of wavefront received at the telescope, i.e., the phase. However only the
low-resolution wavefront gradients can be collected by wavefront sensors. In
this talk, I will discuss how to use regularization methods to reconstruct
high-resolution phase gradients and then use them to recover the phase and the
PSF in high accuracy.

**Speaker:** Clark Dohrmann, Sandia National Laboratories

**Title:** On the Design and Analysis of Coarse Spaces for Domain Decomposition Methods

**Abstract:**

Coarse spaces are at the heart of many domain decomposition methods. In this
talk, we present an overview of the many fruitful and pleasant collaborations
the speaker has had with Olof Widlund in this area during the past 10+ years.
Building on the foundation laid by Dryja, Smith, and Widlund in their 1994
SINUM paper, we describe a family of coarse spaces built on energy minimization
concepts. These spaces have been applied to a variety of problems including
almost incompressible elasticity, irregular shaped subdomains, and problems in
H(curl) and H(div). A hybrid algorithm which combines both overlapping Schwarz
and iterative substructuring concepts will also be discussed. Finally, we
present very recent joint work on the design of small coarse spaces and some
new results for overlapping Schwarz algorithms.

**Speaker:** Hyea Hyun Kim, Kyung Hee University, Korea

**Title:** Adaptive BDDC and FETI-DP algorithms

**Abstract:**

Adaptive BDDC and FETI-DP algorithms are developed for elliptic problems in
both two and three dimensions to deal with highly oscillatory and random
coefficients. For problems with such bad coefficients, the standard choice of
coarse problem often fails to give good performance of both algorithms for such
bad coefficients. The coarse problem is enriched by solving appropriate
generalized eigenvalue problems on each equivalence classes which are edges in
two dimensions, and faces and edges in three dimensions. The condition numbers
of both algorithms with the enriched coarse problem are controlled by the
user-defined tolerance value, which is used to select adaptive coarse
components from the generalized eigenvalue problems. Numerical results are
presented to show the performance of the proposed methods in both two and three
dimensions.

**Speaker:** Axel Klawonn, University of Cologne

**Title:** FETI-DP and BDDC for Composite Materials - Adaptive Coarse Spaces in 3D

**Authors:** Axel Klawonn, Martin Kuehn, Oliver Rheinbach

**Abstract:**

Composite materials are a challenge for domain decomposition methods since
arbitrary material coefficient jumps can lead to a severe deterioration of
their convergence rate. A remedy can be the construction of coarse spaces which
are automatically adapted to those coefficient jumps. In this talk, such coarse
spaces are considered for FETI-DP and BDDC domain decomposition methods which
are based on the adaptive computation of small local eigenvalue problems. A
special emphasis is put on the three dimensional case and on materials with
heterogeneous material parameters where coefficient jumps are not aligned with
the interface of the domain decomposition. Our new approach is based on solving
local eigenvalue problems on faces, enriched by a selected, small number of
additional local eigenvalue problems on edges. The additional edge eigenvalue
problems make the method provably robust with a condition number bound which
depends only on the tolerance of the local eigenvalue problems and some
properties of the domain decomposition. The introduction of relevant edge
eigenvalue problems for FETI-DP and BDDC methods yields a condition number
estimate which is independent of discontinuities of the material parameters.
Deflation and transformation of basis techniques are considered for the
implementation of the adaptively chosen coarse components. Numerical results
are presented for linear elasticity and composite materials supporting
our theoretical findings. The problems considered include those with randomly
distributed coefficients and almost incompressible material components.

**Speaker:** Duk-Soon Oh, Rutgers University

**Title:** Multigrid methods for H(div) with nonoverlapping domain decomposition smoothers

**Abstract:**

We design and analyze V-cycle multigrid methods for H(div) problems
discretized by the lowest order Raviart-Thomas element. Unlike standard
elliptic problems, multigrid methods for the H(div) problems with traditional
smoothers do not work well. We introduce smoothers in the multigrid methods
using nonoverlapping domain decomposition preconditioners that are based on
substructuring. We prove uniform convergence of the V-cycle method.

**Speaker:** Luca Pavarino, University of Pavia

**Title:** Scalable Domain Decomposition Preconditioners for cardiac electro-mechanical simulations

**Authors:** P. Colli Franzone, L. F. Pavarino, S. Scacchi, S. Zampini

**Abstract:**

We introduce and study some scalable domain decomposition preconditioners
for cardiac electro-mechanical 3D simulations. The cardiac electro-mechanical
model considered consisting of four coupled components: a) the quasi-static
transversely isotropic finite elasticity equations for the deformation of the
cardiac tissue; b) the active tension model for the intracellular calcium
dynamics and cross-bridge binding; c) the anisotropic Bidomain model for the
electrical current flow through the deforming cardiac tissue; d) the membrane
model of ventricular myocytes, including stretch-activated channels. The 3D
numerical simulations are based on our finite element parallel solver, which
employs Multilevel Additive Schwarz preconditioners for the solution of the
discretized Bidomain equations and Newton-Krylov methods with AMG or BDDC
preconditioners for the solution of the discretized nonlinear finite elasticity
equations. The results of several parallel simulations show the scalability of
both linear and nonlinear solvers and their application to the study of
re-entrant waves in the presence of different mechano-electrical feedbacks.

**Speaker:** Oliver Rheinbach, TU Bergakademie Freiberg

**Title:** Domain Decomposition for Extreme Scale Computing

**Abstract:**

Different Versions of Nonlinear Domain Decomposition Methods (DDM) are
discussed which scale to the largest supercomputers currently available. This
includes Nonlinear BDDC and FETI-DP methods applying multigrid methods for the
coarse problem or for, both, the subdomain problems as well as the coarse
problem. In these method, the subdomain problems are nonlinear which reduces
communication and can help to localize the computational work. Moreover,
numerical results for a highly parallel numerical homogenization method well
known in nonlinear structural mechanics (FE^{2}) are presented applying FETI-DP
domain decomposition methods on the Representative Volume Elements (RVEs).

**Speaker:** Marcus Sarkis, Worcester Polytechnic Institute

**Title:** Robust Discretizations based on Adaptive Selection of Primal Constraints

**Abstract:**

Major progress has been made recently to make FETI-DP and BDDC preconditioners
robust with respect to any variation of coefficients inside and/or across the
subdomains. A reason for this success is the adaptive selection of primal
constraints technique based on localized generalized eigenvalue problems. In
this talk we discuss how to transfer this technique to the field of
discretizations. We design discretizations where the number of degrees of
freedom is the number of primal constraints on the coarse triangulation. We
establish a priori energy error estimates with hidden constants independently
of the coefficients, and for the analysis, the regularity of the solution is
not used, only that the right-hand side be in L2. We note that the resulting
multiscale basis functions are nonlocal however decay exponentially. In this
talk we concentrate on the Raviart-Thomas case. (Joint work with Alexandre
Madureira, National Laboratory for Scientific Computing, Brazil)

**Speaker:** Simone Scacchi, University of Milan

**Title:** BDDC preconditioners for isogeometric analysis

**Authors:** L. Beirao da Veiga, D. Cho, L. F. Pavarino, S. Scacchi, S. Zampini, O. B. Widlund

**Abstract:**

Isogeometric Analysis (IGA) is an innovative numerical technology for the
solution of Partial Differential Equations (PDEs), where the geometry
description of the PDE domain is adopted from a Computer Aided Design (CAD)
parametrization usually based on Non-Uniform Rational B-Splines (NURBS) and the
same NURBS basis functions are also used as the PDEs discrete basis, following
an isoparametric paradigm. The aim of this talk is to present Balancing Domain
Decomposition by Constraints (BDDC) preconditioners for IGA discretizations of
scalar elliptic problems and compressible linear elasticity, based on three
types of interface averaging functions: standard ρ-scaling, stiffness
scaling and the novel deluxe scaling, with either full or reduced set of primal
constraints. The resulting algorithms are proved to be quasi-optimal, scalable
and robust with respect to jumps of the PDEs coefficients. Extensive two- and
three-dimensional numerical results validate the theoretical estimates.

**Speaker:** Barry Smith, Argonne National Laboratory

**Title:** Composability in algebraic solvers and ODE integrators
(canceled)

**Abstract:**

It is by now relatively commonly known that most efficient linear
preconditioners can be obtained by composing a small set of simple operations,
what is less well understood is that this also holds true for nonlinear solvers
as well as ODE integrators. I will discuss composability at all three levels
and how it can simplify the development of convergence results and numerical
solver libraries.

**Speaker:** Nicole Spillane, Ecole Polytechnique

**Title:** Adaptive Multipreconditioning for Symmetric and Non-Symmetric Problems

**Abstract:**

Multipreconditioning is a technique that allows to use multiple preconditioners
within a Krylov subspace method. For domain decomposition, this means that each
contribution to the preconditioner (generated by one subdomain) is used to
enlarge the search space instead of the sum of all of these directions. Quite
naturally, this significantly enlarged search space leads to robust solvers
that converge in a small number of iterations. In order for the overall cost of
computation to be competitive, adaptivity is needed: only some iterations of
the Krylov subspace methods are multipreconditioned. In this talk I will
discuss how to choose the adaptivity process and what results can be guaranteed
depending on the Domain Decomposition method and the nature of the linear
system (symmetric or nonsymmetric).

**Speaker:** Daniel Szyld, Temple University

**Title:** Asynchronous Optimized Schwarz, Theory and Experiments

**Abstract:**

Asynchronous methods refer to parallel iterative procedures where
each process performs its task without waiting for other processes to be
completed, i.e., with whatever information it has locally available and with no
synchronizations with other processes. In this talk, an asynchronous version of
the optimized Schwarz method is presented for the solution of differential
equations on a parallel computational environment. In a one-way subdivision of
the computational domain, with overlap, the method is shown to converge when
the optimal artificial interface conditions are used. Convergence is also
proved under very mild conditions on the size of the subdomains, when
approximate (non-optimal) interface conditions are utilized. Numerical results
are presented on large three-dimensional problems illustrating the efficiency
of the proposed asynchronous parallel implementation of the method. The main
application shown is the calculation of the gravitational potential in the area
around the Chicxulub crater, in Yucatan, where an asteroid is believed to have
landed 66 million years ago contributing to the extinction of the dinosaurs.
(Joint work with Frédéric Magoulès and Cedric Venet, CentraleSupélec, Châtenay-Malabry, France)

**Speaker:** Xuemin Tu, University of Kansas

**Title:** BDDC domain decomposition for hybrid discontinuous Galerkin Methods

**Abstract:**

A Balancing domain decomposition by constraints (BDDC) algorithm is studied for
solutions of large sparse linear algebraic systems arising from hybrid
discontinuous Galerkin discretization. The condition number for the
preconditioned system is estimated and numerical results are provided to
confirm the results.

**Speaker:** Barbara Wohlmuth, TU Munich

**Title:** Domain decomposition meets multigrid

**Abstract:**

We discuss classical tearing and interconnecting strategies in combination with
reduced order modeling, adaptive strategies and large scale multigrid solvers.
The concepts of overlapping domain decomposition techniques are applied to
eigenvalue problems in structural mechanics. A greedy algorithm is used to set
up a reduced basis for rather large multi-storey timber construction. Material
parameters enter by the wall type and elastomer. The abstract framework of
non-overlapping Dirichlet-Neumann or Dirichlet-Dirichlet components is used in
combination with over-balancing techniques to design fault robust multigrid
solver. The reconnecting step is controlled by an hierarchical error estimator
accounting for the algebraic error and a residual type one for the
discretization error.

**Speaker:** Jinchao Xu, Pennsylvania State University

**Title:** Overlapping Schwarz Methods with Randomized Ordering

**Abstract:**

We consider the iterative method of subspace corrections, especially
overlapping Schwarz methods, with random ordering. We prove identities for the
expected convergence rate, which can provide sharp estimates for the error
reduction per iteration. We also study the fault-tolerant feature of the
randomized successive subspace correction method by simply rejecting all the
corrections when error occurs and show that the results iterative method
converges with probability 1. Moreover, we also provide sharp estimates on the
expected convergence rate for the fault-tolerant, randomized, subspace
correction method.

**Speaker:** Stefano Zampini, KAUST

**Title:** On the robustness and prospects of BDDC and FETI-DP
methods for finite element discretizations of elliptic PDEs

**Abstract:**

In the last decade, Balancing Domain Decomposition by Constraints (BDDC) and
Finite Element Tearing and Interconnecting Dual-Primal (FETI-DP) methods have
proven to be powerful solvers for large and sparse linear systems arising from
the finite element discretization of elliptic PDEs. Condition number bounds can
be theoretically established, and these bounds are independent of the number of
subdomains of the decomposition, and, more important, on the heterogeneity of
the coefficients of the PDE. After a brief introduction to the methods, I will
present the current state of their implementation in the PETSc library,
together with numerical results for a variety of finite element discretizations
and partial differential equations. Robustness, algorithmic aspects, and
prospects of these methods will be also discussed.