George Biros

University of Texas at Austin, Austin, Texas, United States

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Publications (87)66.05 Total impact

  • Bryan Quaife, George Biros
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    ABSTRACT: We present an adaptive arbitrary-order accurate time-stepping numerical scheme for the flow of vesicles suspended in Stokesian fluids. Our scheme can be summarized as an approximate implicit spectral deferred correction (SDC) method. Applying a textbook fully implicit SDC scheme to vesicle flows is prohibitively expensive. For this reason we introduce several approximations. Our scheme is based on a semi-implicit linearized low-order time stepping method. (Our discretization is spectrally accurate in space.) We also use invariant properties of vesicle flows, constant area and boundary length in two dimensions, to reduce the computational cost of error estimation for adaptive time stepping. We present results in two dimensions for single-vesicle flows, constricted geometry flows, converging flows, and flows in a Couette apparatus. We experimentally demonstrate that the proposed scheme enables automatic selection of the step size and high-order accuracy.
    05/2014;
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    Hari Sundar, Georg Stadler, George Biros
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    ABSTRACT: We present a comparison of different multigrid approaches for the solution of systems arising from high-order continuous finite element discretizations of elliptic partial differential equations on complex geometries. We consider the pointwise Jacobi, the Chebyshev-accelerated Jacobi and the symmetric successive over-relaxation (SSOR) smoothers, as well as elementwise block Jacobi smoothing. Three approaches for the multigrid hierarchy are compared: 1) high-order $h$-multigrid, which uses high-order interpolation and restriction between geometrically coarsened meshes; 2) $p$-multigrid, in which the polynomial order is reduced while the mesh remains unchanged, and the interpolation and restriction incorporate the different-order basis functions; and 3), a first-order approximation multigrid preconditioner constructed using the nodes of the high-order discretization. This latter approach is often combined with algebraic multigrid for the low-order operator and is attractive for high-order discretizations on unstructured meshes, where geometric coarsening is difficult. Based on a simple performance model, we compare the computational cost of the different approaches. Using scalar test problems in two and three dimensions with constant and varying coefficients, we compare the performance of the different multigrid approaches for polynomial orders up to 16. Overall, both $h$- and $p$-multigrid work well; the first-order approximation is less efficient. For constant coefficients, all smoothers work well. For variable coefficients, Chebyshev and SSOR smoothing outperforms Jacobi smoothing. While all of the tested methods converge in a mesh-independent number of iterations, none of them behaves completely independent of the polynomial order. When multigrid is used as a preconditioner in a Krylov method, the iteration number decreases significantly compared to using multigrid as a solver.
    02/2014;
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    Bryan Quaife, George Biros
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    ABSTRACT: We consider numerical algorithms for the simulation of the rheology of two-dimensional vesicles suspended in a viscous Stokesian fluid. The vesicle evolution dynamics is governed by hydrodynamic and elastic forces. The elastic forces are due to local inextensibility of the vesicle membrane and resistance to bending. Numerically resolving vesicle flows poses several challenges. For example, we need to resolve moving interfaces, address stiffness due to bending, enforce the inextensibility constraint, and efficiently compute the (non-negligible) long-range hydrodynamic interactions. Our method is based on the work of {\em Rahimian, Veerapaneni, and Biros, "Dynamic simulation of locally inextensible vesicles suspended in an arbitrary two-dimensional domain, a boundary integral method", Journal of Computational Physics, 229 (18), 2010}. It is a boundary integral formulation of the Stokes equations coupled to the interface mass continuity and force balance. We extend the algorithms presented in that paper to increase the robustness of the method and enable simulations with concentrated suspensions. In particular, we propose a scheme in which both intra-vesicle and inter-vesicle interactions are treated semi-implicitly. In addition we use special integration for near-singular integrals and we introduce a spectrally accurate collision detection scheme. We test the proposed methodologies on both unconfined and confined flows for vesicles whose internal fluid may have a viscosity contrast with the bulk medium. Our experiments demonstrate the importance of treating both intra-vesicle and inter-vesicle interactions accurately.
    Journal of Computational Physics. 09/2013; 274.
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    Bryan Quaife, George Biros
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    ABSTRACT: The discretization of the double-layer potential integral equation for the interior Dirichlet Laplace problem in a domain with smooth boundary results in a linear system that has a bounded condition number. Thus, the number of iterations required for the convergence of a Krylov method is, asymptotically, independent of the discretization size $N$. Using the Fast Multipole Method (FMM) to accelerate the matrix-vector products, we obtain an optimal $\bigO(N)$ solver. I practice, however, when the geometry is complicated, the number of Krylov iterations behaves in an $N$-dependent manner and can be quite large. In many applications, such cost is prohibitively expensive. There is a need, therefore, for designing preconditioners that reduce the number of Krylov iterations. We summarize the different methodologies that have appeared in the literature (single-grid, multigrid, approximate sparse inverses) and we propose a new class of preconditioners based on an FMM-based spatial decomposition of the double-layer operator. We present an experimental study in which we compare the different approaches and we discuss the merits and shortcomings of our approach.
    Numerical Linear Algebra with Applications 08/2013; · 1.20 Impact Factor
  • Hari Sundar, Dhairya Malhotra, George Biros
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    ABSTRACT: In this paper, we present HykSort, an optimized comparison sort for distributed memory architectures that attains more than 2× improvement over bitonic sort and samplesort. The algorithm is based on the hypercube quicksort, but instead of a binary recursion, we perform a k-way recursion in which the pivots are selected accurately with an iterative parallel select algorithm. The single-node sort is performed using a vectorized and multithreaded merge sort. The advantages of HykSort are lower communication costs, better load balancing, and avoidance of O(p)-collective communication primitives. We also present a staged communication samplesort, which is more robust than the original samplesort for large core counts. We conduct an experimental study in which we compare hypercube sort, bitonic sort, the original samplesort, the staged samplesort, and HykSort. We report weak and strong scaling results and study the effect of the grain size. It turns out that no single algorithm performs best and a hybridization strategy is necessary. As a highlight of our study, on our largest experiment on 262,144 AMD cores of the CRAY XK7 "Titan" platform at the Oak Ridge National Laboratory we sorted 8 trillion 32-bit integer keys in 37 seconds achieving 0.9TB/s effective throughput.
    Proceedings of the 27th international ACM conference on International conference on supercomputing; 06/2013
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    ABSTRACT: We present a generative approach for simultaneously registering a probabilistic atlas of a healthy population to brain magnetic resonance (MR) scans showing glioma and segmenting the scans into tumor as well as healthy tissue labels. The proposed method is based on the expectation maximization (EM) algorithm that incorporates a glioma growth model for atlas seeding, a process which modifies the original atlas into one with tumor and edema adapted to best match a given set of patient's images. The modified atlas is registered into the patient space and utilized for estimating the posterior probabilities of various tissue labels. EM iteratively refines the estimates of the posterior probabilities of tissue labels, the deformation field and the tumor growth model parameters. Hence, in addition to segmentation, the proposed method results in atlas registration and a low-dimensional description of the patient scans through estimation of tumor model parameters. We validate the method by automatically segmenting 10 MR scans and comparing the results to those produced by clinical experts and two state-of-the-art methods. The resulting segmentations of tumor and edema outperform the results of the reference methods, and achieve a similar accuracy from a second human rater. We additionally apply the method to 122 patients scans and report the estimated tumor model parameters and their relations with segmentation and registration results. Based on the results from this patient population, we construct a statistical atlas of the glioma by inverting the estimated deformation fields to warp the tumor segmentations of patients scans into a common space.
    IEEE transactions on medical imaging. 08/2012; 31(10):1941-54.
  • Stéphanie Chaillat, George Biros
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    ABSTRACT: We propose an algorithm to compute an approximate singular value decomposition (SVD) of least-squares operators related to linearized inverse medium problems with multiple events. Such factorizations can be used to accelerate matrix-vector multiplications and to precondition iterative solvers.We describe the algorithm in the context of an inverse scattering problem for the low-frequency time-harmonic wave equation with broadband and multi-point illumination. This model finds many applications in science and engineering (e.g., seismic imaging, subsurface imaging, impedance tomography, non-destructive evaluation, and diffuse optical tomography).We consider small perturbations of the background medium and, by invoking the Born approximation, we obtain a linear least-squares problem. The scheme we describe in this paper constructs an approximate SVD of the Born operator (the operator in the linearized least-squares problem). The main feature of the method is that it can accelerate the application of the Born operator to a vector.If Nω is the number of illumination frequencies, Ns the number of illumination locations, Nd the number of detectors, and N the discretization size of the medium perturbation, a dense singular value decomposition of the Born operator requires O(min(NsNωNd,N)]2×max(NsNωNd,N))O(min(NsNωNd,N)]2×max(NsNωNd,N)) operations. The application of the Born operator to a vector requires O(NωNsμ(N))O(NωNsμ(N)) work, where μ(N) is the cost of solving a forward scattering problem. We propose an approximate SVD method that, under certain conditions, reduces these work estimates significantly. For example, the asymptotic cost of factorizing and applying the Born operator becomes O(μ(N)Nω)O(μ(N)Nω). We provide numerical results that demonstrate the scalability of the method.
    Journal of Computational Physics 06/2012; 231(12):4403–4421. · 2.14 Impact Factor
  • Wei Zhu, Sung Ha Kang, George Biros
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    ABSTRACT: We propose a novel geodesic-active-contour-based (GAC-based) variational model that uses two level-set functions to segment the right and left ventricles and the epicardium in short-axis magnetic resonance (MR) images. For the right ventricle, the myocardial wall is typically very thin and hard to identify using the resolution of existing MR scanners. We propose to use two level sets to identify both the endocardial wall by pushing away one level-set function from another, in the setting of the edge-driven GAC model with a new edge detection function. Existing edge detection functions have strict restrictions on the location of initial contours. We develop a new edge detection function that relaxes this restriction and propose an iterative method that uses a sequence of edge detection functions to minimize the energy of our model successively. Experimental results are presented to validate the effectiveness of the proposed model.
    International Journal of Computer Mathematics 06/2012; 2012(1–16). · 0.54 Impact Factor
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    ABSTRACT: We present a parallel multigrid method for solving variable-coefficient elliptic partial differential equations on arbitrary geometries using highly adapted meshes. Our method is designed for meshes that are built from an unstructured hexa-hedral macro mesh, in which each macro element is adaptively refined as an octree. This forest-of-octrees approach enables us to generate meshes for complex geometries with arbitrary levels of local refinement. We use geometric multigrid (GMG) for each of the octrees and algebraic multigrid (AMG) as the coarse grid solver. We designed our GMG sweeps to entirely avoid collectives, thus minimizing communication cost. We present weak and strong scaling results for the 3D variable-coefficient Poisson problem that demonstrate high parallel scalability. As a highlight, the largest problem we solve is on a non-uniform mesh with 100 billion unknowns on 262,144 cores of NCCS's Cray XK6 "Jaguar" in this solve we sustain 272 TFlops/s.
    High Performance Computing, Networking, Storage and Analysis (SC), 2012 International Conference for; 01/2012
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    ABSTRACT: This study focuses numerically on dynamics in two dimensions of vesicles in microcirculation. The method used is based on boundary integral formulation. This study is inspired by the behavior of red blood cells (RBCs) in the microvasculature. Red RBCs carry oxygen from the lungs and deliver it through the microvasculature. The shape adopted by RBCs can affect blood flow and influence oxygen delivery. Our simulation using vesicles (a simple model for RBC) reveals unexpected complexity as compared to the case where a purely unbounded Poiseuille flow is considered [Kaoui, Biros, and Misbah, Phys. Rev. Lett. 103, 188101 (2009)]. In sufficiently large channels (in the range of 100 μm; the vesicle size and its reduced volume are taken in the range of those of a human RBC), such as arterioles, a slipperlike (asymmetric) shape prevails. A parachutelike (symmetric) shape is adopted in smaller channels (in the range of 20 μm, as in venules), but this shape loses stability and again changes to a pronounced slipperlike morphology in channels having a size typical of capillaries (5-10 μm). Stiff membranes, mimicking malaria infection, for example, adopt a centered or off-centered snakelike locomotion instead (the denomination snaking is used for this regime). A general scenario of how and why vesicles adopt their morphologies and dynamics among several distinct possibilities is provided. This finding potentially points to nontrivial RBCs dynamics in the microvasculature.
    Physical Review E 10/2011; 84(4 Pt 1):041906. · 2.31 Impact Factor
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    ABSTRACT: Recent evidence has suggested that the presence and proliferation of vasa vasorum (VV) in the plaque is correlated to an increase in plaque inflammation and destabilization, leading to acute coronary events (e.g., heart attacks). Therefore, the detection and quantification of VV in plaque (i.e., extra luminal blood perfusion) is an important problem since it may enable the development of an index of plaque vulnerability. In this paper, we explore the feasibility of a method that employs a physics-based model of the scattered intravascular ultrasound (IVUS) radio frequency signal for the detection of blood. We evaluate our method using synthetic data and validate it using six 40 MHz pullback sequences acquired with three different IVUS systems from different arteries of rabbits and swines. Our experimental results are very promising and indicate the feasibility of our method for the computation of a feature that leads to automatic extra-luminal blood detection which may be an indication of plaque inflammation.
    Medical image computing and computer-assisted intervention : MICCAI ... International Conference on Medical Image Computing and Computer-Assisted Intervention. 01/2011; 14(Pt 1):396-403.
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    ABSTRACT: Cross-streamline migration of deformable entities is essential in many problems such as industrial particulate flows, DNA sorting, and blood rheology. Using two-dimensional numerical experiments, we have discovered that vesicles suspended in a flow with curved flow lines migrate towards regions of high flowline curvature, which are regions of high shear rates. The migration velocity of a vesicle is found to be a universal function of the normal stress difference and the flow curvature. This finding quantitatively demonstrates a direct coupling between a microscopic quantity (migration) and a macroscopic one (normal stress difference). Furthermore, simulations with multiple vesicles revealed a self-organization, which corresponds to segregation, in a rim closer to the inner cylinder, resulting from a subtle interaction among vesicles. Such segregation effects could have a significant impact on the rheology of vesicle flows.
    Physical Review Letters 01/2011; 106(2):028101. · 7.73 Impact Factor
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    ABSTRACT: Clustering and nearest neighbor searches in high dimensions are fundamental components of computational geometry, computational statistics, and pattern recognition. Despite the widespread need to analyze massive datasets, no MPI-based implementations are available to allow this analysis to be scaled to modern highly parallel platforms. We seek to develop a set of algorithms that will provide unprecedented scalability and performance for these fundamental problems.
    Conference on High Performance Computing Networking, Storage and Analysis - Companion Volume, SC 2011, Seattle, WA, USA, November 12-18, 2011; 01/2011
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    IEEE Trans. Med. Imaging. 01/2011; 30:375-390.
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    ABSTRACT: Vesicles are locally-inextensible fluid membranes that can sustain bending. In this paper, we extend the study of Veerapaneni et al. [S.K. Veerapaneni, D. Gueyffier, G. Biros, D. Zorin, A numerical method for simulating the dynamics of 3D axisymmetric vesicles suspended in viscous flows, Journal of Computational Physics 228 (19) (2009) 7233–7249] to general non-axisymmetric vesicle flows in three dimensions.Although the main components of the algorithm are similar in spirit to the axisymmetric case (spectral approximation in space, semi-implicit time-stepping scheme), important new elements need to be introduced for a full 3D method. In particular, spatial quantities are discretized using spherical harmonics, and quadrature rules for singular surface integrals need to be adapted to this case; an algorithm for surface reparameterization is needed to ensure stability of the time-stepping scheme, and spectral filtering is introduced to maintain reasonable accuracy while minimizing computational costs. To characterize the stability of the scheme and to construct preconditioners for the iterative linear system solvers used in the semi-implicit time-stepping scheme, we perform a spectral analysis of the evolution operator on the unit sphere.By introducing these algorithmic components, we obtain a time-stepping scheme that circumvents the stability constraint on the time-step and achieves spectral accuracy in space. We present results to analyze the cost and convergence rates of the overall scheme. To illustrate the applicability of the new method, we consider a few vesicle-flow interaction problems: a single vesicle in relaxation, sedimentation, shear flows, and many-vesicle flows.
    Journal of Computational Physics 01/2011; 230:5610-5634. · 2.14 Impact Factor
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    ABSTRACT: This paper presents an approach for joint segmentation and deformable registration of brain scans of glioma patients to a normal atlas. The proposed method is based on the Expectation Maximization (EM) algorithm that incorporates a glioma growth model for atlas seeding, a process which modifies the normal atlas into one with a tumor and edema. The modified atlas is registered into the patient space and utilized for the posterior probability estimation of various tissue labels. EM iteratively refines the estimates of the registration parameters, the posterior probabilities of tissue labels and the tumor growth model parameters. We have applied this approach to 10 glioma scans acquired with four Magnetic Resonance (MR) modalities (T1, T1-CE, T2 and FLAIR) and validated the result by comparing them to manual segmentations by clinical experts. The resulting segmentations look promising and quantitatively match well with the expert provided ground truth.
    Medical image computing and computer-assisted intervention : MICCAI ... International Conference on Medical Image Computing and Computer-Assisted Intervention. 01/2011; 14(Pt 2):532-40.
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    ABSTRACT: This paper investigates the problem of atlas registration of brain images with gliomas. Multiparametric imaging modalities (T1, T1-CE, T2, and FLAIR) are first utilized for segmentations of different tissues, and to compute the posterior probability map (PBM) of membership to each tissue class, using supervised learning. Similar maps are generated in the initially normal atlas, by modeling the tumor growth, using reaction-diffusion equation. Deformable registration using a demons-like algorithm is used to register the patient images with the tumor bearing atlas. Joint estimation of the simulated tumor parameters (e.g., location, mass effect and degree of infiltration), and the spatial transformation is achieved by maximization of the log-likelihood of observation. An expectation-maximization algorithm is used in registration process to estimate the spatial transformation and other parameters related to tumor simulation are optimized through asynchronous parallel pattern search (APPSPACK). The proposed method has been evaluated on five simulated data sets created by statistically simulated deformations (SSD), and fifteen real multichannel glioma data sets. The performance has been evaluated both quantitatively and qualitatively, and the results have been compared to ORBIT, an alternative method solving a similar problem. The results show that our method outperforms ORBIT, and the warped templates have better similarity to patient images.
    IEEE transactions on medical imaging. 09/2010; 30(2):375-90.
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    A. Gooya, G. Biros, C. Davatzikos
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    ABSTRACT: This paper investigates the problem of atlas registration of brain images with tumors. Multi-parametric imaging modalities are first utilized for segmentations of different tissues, and to compute the posterior probability map (PBM) of membership to each tissue class, using supervised learning. Similar maps are generated in the initially normal atlas, by modeling the tumor growth. An Expectation-Maximization algorithm is used to estimate the spatial transformation and other parameters related to tumor simulation are optimized through Asynchronous Parallel Pattern Search (APPSPACK). The proposed method has been evaluated on simulated data sets created by Statistically Simulated Deformations (SSD), and real multichannel Glioma data sets. The performance has been evaluated both quantitatively and qualitatively. The results show that our method is promising to achieve a good similarity between the warped templates and patient images.
    Computer Vision and Pattern Recognition Workshops (CVPRW), 2010 IEEE Computer Society Conference on; 07/2010
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    ABSTRACT: This work presents the first extensive study of single-node performance optimization, tuning, and analysis of the fast multipole method (FMM) on modern multi-core systems. We consider single- and double-precision with numerous performance enhancements, including low-level tuning, numerical approximation, data structure transformations, OpenMP parallelization, and algorithmic tuning. Among our numerous findings, we show that optimization and parallelization can improve double-precision performance by 25× on Intel's quad-core Nehalem, 9.4× on AMD's quad-core Barcelona, and 37.6× on Sun's Victoria Falls (dual-sockets on all systems). We also compare our single-precision version against our prior state-of-the-art GPU-based code and show, surprisingly, that the most advanced multicore architecture (Nehalem) reaches parity in both performance and power efficiency with NVIDIA's most advanced GPU architecture.
    Parallel & Distributed Processing (IPDPS), 2010 IEEE International Symposium on; 05/2010
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    ABSTRACT: This project addressed the statistical inverse problem of reconstruction of an uncertain shape of a scatterer or properties of a medium from noisy observations of scattered wavefields. The Bayesian solution of this inverse problem yields a posterior pdf, requiring the solution of the forward wave equation to evaluate the probability of any point in parameter space. The standard approach is to sample this pdf via an MCMC method and then compute statistics of the samples. However, standard MCMC methods view the underlying parameter-to-observable map as a black box, and thus do not exploit its structure, becoming prohibitive for high dimensional parameter spaces and expensive simulations. A preconditioned Langevin-accelerated MCMC method for sampling high-dimensional PDE-based probability densities was developed. The preconditioner exploits local Hessian (of the negative log posterior) information to greatly speed up sampling, leading to a stochastic version of Newton's method. Fast Hessian approximations were developed for several inverse scattering problems. Applications to model inverse medium scattering problems indicated several orders of magnitude improvement over a reference black-box MCMC method.
    02/2010;

Publication Stats

1k Citations
66.05 Total Impact Points

Institutions

  • 2011–2013
    • University of Texas at Austin
      • Institute for Computational Engineering and Sciences
      Austin, Texas, United States
  • 2009–2011
    • University Joseph Fourier - Grenoble 1
      • Laboratoire Interdisciplinaire de Physique
      Grenoble, Rhône-Alpes, France
  • 2004–2011
    • University of Pennsylvania
      • • Department of Radiology
      • • Department of Bioengineering
      • • Department of Mechanical Engineering and Applied Mechanics
      Philadelphia, PA, United States
  • 1970–2011
    • Georgia Institute of Technology
      • • Department of Biomedical Engineering
      • • School of Computational Science & Engineering
      • • College of Computing
      Atlanta, Georgia, United States
  • 2002–2004
    • CUNY Graduate Center
      New York City, New York, United States
  • 1999
    • Carnegie Mellon University
      Pittsburgh, Pennsylvania, United States