Shankar Sastry

Shankar Sastry
Google LLC

Ph.D.

About

28
Publications
5,262
Reads
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202
Citations
Introduction
Shankar Sastry currently works at Google. Shankar's research includes the areas of geometric modeling, mesh generation, computational geometry, high-performance computing, and scientific computing.
Additional affiliations
September 2012 - March 2016
University of Utah
Position
  • PostDoc Position
June 2010 - August 2010
Argonne National Laboratory
Position
  • Research Intern
August 2007 - August 2012
Pennsylvania State University
Position
  • Research Assistant

Publications

Publications (28)
Article
Full-text available
The presence of a few inverted or poor-quality mesh elements can negatively affect the stability, convergence and efficiency of a finite element solver and the accuracy of the associated partial differential equation solution. We propose a mesh quality improvement and untangling method that untangles a mesh with inverted elements and improves its q...
Article
Full-text available
We propose a new strategy for boundary conforming meshing that decouples the problem of building tetrahedra of proper size and shape from the problem of conforming to complex, non-manifold boundaries. This approach is motivated by the observation that while several methods exist for adaptive tetrahedral meshing, they typically have difficulty at ge...
Conference Paper
Full-text available
Interpolation techniques are used to estimate function values and their derivatives at those points for which a numerical solution of any equation is not explicitly evaluated. In particular, the shape functions are used to interpolate a solution (within an element) of a partial differential equation obtained by the finite element method. Mesh gener...
Conference Paper
Full-text available
We consider the problem of inserting a vertex inside a star-shaped input polygon at the location that maximizes the minimum angle in the resulting triangulation. An existing polynomial-time algorithm solves for the intersection of three polynomial surfaces (a prior paper indicates that these are eighth-degree polynomials) and computes the maxima of...
Preprint
Full-text available
I present a generalization of Chew's first algorithm for Delaunay mesh refinement. In his algorithm, Chew splits the line segments of the input planar straight line graph (PSLG) into shorter subsegments whose lengths are nearly identical. The constrained Delaunay triangulation of the subsegments is refined based on the length of the radii of the ci...
Preprint
Full-text available
I present a 3D advancing-front mesh refinement algorithm that generates a constrained Delaunay mesh for any piecewise linear complex (PLC) and extend this algorithm to produce truly Delaunay meshes for any PLC. First, as in my recently published 2D algorithm, I split the input line segments such that the length of the subsegments is asymptotically...
Article
Full-text available
I present a generalization of Chew's first algorithm for Delaunay mesh refinement. I split the line segments of an input planar straight line graph (PSLG) such that the lengths of split segments are asymptotically proportional to the local feature size at their endpoints. By employing prior algorithms, I then refine the truly or constrained Delauna...
Article
Full-text available
We propose a novel deviation-based vertex reordering method for 2D mesh quality improvement. We reorder free vertices based on how likely this is to improve the quality of adjacent elements, based on the gradient of the element quality with respect to the vertex location. Specifically, we prioritize the free vertex with large differences between th...
Article
Full-text available
Mesh generation and adaptive refinement are largely driven by the objective of minimizing the bounds on the interpolation error of the solution of the partial differential equation (PDE) being solved. Thus, the characterization and analysis of interpolation error bounds for curved, high-order finite elements is often desired to efficiently obtain t...
Article
Full-text available
We present a new iterative technique based on radial basis function (RBF) interpolation and smoothing for the generation and smoothing of curvilinear meshes from straight-sided or other curvilinear meshes. Our technique approximates the coordinate deformation maps in both the interior and boundary of the curvilinear output mesh by using only scatte...
Article
Full-text available
For visualization and finite element mesh generation, feature-preserving meshing of piecewise-smooth implicit surfaces has been a challenge since the marching cubes technique was introduced in the 1980s. Such tessellation-based techniques have been used with varying degrees of success for this purpose, but they have consistently failed to reproduce...
Conference Paper
Full-text available
High-order, curvilinear meshes have recently become popular due to their ability to conform to the geometry of the domain. Curvilinear meshes are generated by first constructing a straight-sided mesh and then curving the boundary elements (and, consequently, some of the interior edges and faces) to respect the geometry of the domain. The locations...
Article
Paper withdraw due to incorrect proofs. Work in progress. One of the objectives of a Delaunay mesh refinement algorithm is to produce meshes with tetrahedral elements having a bounded aspect ratio, which is the ratio between the radius of the circumscribing and inscribing spheres. The refinement is carried out by inserting additional Steiner verti...
Article
Full-text available
The development of parallel algorithms for mesh generation, untangling, and quality improvement is of high importance due to the need for large meshes with millions to billions of elements and the availability of supercomputers with hundreds to thousands of cores. There have been prior efforts in the development of parallel algorithms for mesh gene...
Article
Full-text available
Solving partial differential equations using finite element (FE) methods for unstructured meshes that contain billions of elements is computationally a very challenging task. While parallel implementations can deliver a solution in a reasonable amount of time, they suffer from low cache utilization due to unstructured data access patterns. In this...
Article
Full-text available
A computational methodology for simulating virtual inferior vena cava (IVC) filter placement and IVC hemodynamics was developed and demonstrated in two patient-specific IVC geometries: a left-sided IVC and an IVC with a retroaortic left renal vein. An inverse analysis was performed to obtain the approximate in vivo stress state for each patient vei...
Conference Paper
Full-text available
A computational methodology for simulating inferior vena cava (IVC) filter placement and IVC hemodynamics was developed and tested on two patient-specific IVC geometries: a left-sided IVC, and an IVC with a retroaortic left renal vein. Virtual IVC filter placement was performed with finite element analysis (FEA) using non-linear material models and...
Conference Paper
Full-text available
Introduction: Pulmonary embolism (PE) is a potentially life-threatening condition in which an embolus obstructs pulmonary blood flow, usually as a result of deep vein thrombosis (DVT) or trauma. Anticoagulant therapy is often used to prevent PE in patients who are at risk. When anticoagulants are contraindicated, an inferior vena cava (IVC) filter...
Conference Paper
Full-text available
Pulmonary embolism (PE) is a potentially life‐threatening condition in which an embolus obstructs pulmonary blood flow, usually as a result of deep vein thrombosis (DVT) or trauma. Anticoagulant therapy is often used to prevent PE in patients who are at risk. When anticoagulants are contraindicated, an inferior vena cava (IVC) filter may be implant...
Chapter
Pulmonary embolism (PE) is a potentially-fatal disease in which blood clots (i.e., emboli) break free from the deep veins in the body and migrate to the lungs. In order to prevent PE, anticoagulation therapy is often used; however, for some patients, it is contraindicated. For such patients, a mechanical filter, namely an inferior vena cava (IVC) f...
Article
Full-text available
We characterize the performance of gradient- and Hessian-based optimization methods for mesh quality improvement. In particular, we consider the steepest descent and Polack-Ribière conjugate gradient methods which are gradient based. In the Hessian-based category, we consider the quasi-Newton, trust region, and feasible Newton methods. These techni...
Conference Paper
Full-text available
The presence of a few poor-quality mesh elements can negatively affect the stability and efficiency of a finite element solver and the accuracy of the associated partial differential equation solution. We propose a mesh quality improvement method that improves the quality of the worst elements. Mesh quality improvement of the worst elements can be...
Article
Full-text available
In this paper, we study the effect of the choice of mesh quality metric, preconditioner, and sparse linear solver on the numerical solution of elliptic partial differential equations (PDEs). We smooth meshes on several geometric domains using various quality metrics and solve the associated elliptic PDEs using the finite element method. The resulti...
Chapter
Full-text available
In this paper, we study the effect the choice of mesh quality metric, preconditioner, and sparse linear solver have on the numerical solution of elliptic partial differential equations (PDEs). We smoothe meshes on several geometric domains using various quality metrics and solve the associated elliptic PDEs using the finite element method. The resu...
Chapter
Full-text available
Discretization methods, such as the finite element method, are commonly used in the solution of partial differential equations (PDEs). The accuracy of the computed solution to the PDE depends on the degree of the approximation scheme, the number of elements in the mesh [1], and the quality of the mesh [2, 3]. More specifically, it is known that as...

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