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- RPI SCOREC - Technical Reports

Reality Abstract The lack of data on in vivo material properties of soft tissues has been a significant impediment in the development of virtual reality based surgical simulators that can provide the user with realistic visual and haptic feedback As a first step towards characterizing the mechanical behavior of organs this work presents in vivo force response of the liver and lower esophagus of pigs when subjected to ramp and

Original URL path: http://www.scorec.rpi.edu/reports/view_report.php?id=312 (2015-07-15)

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medical personnel due to extremely high computational speed required for realistic simulation in real time there is a fundamental trade off between realism and processing speed of the simulator Our research focuses on how we can optimally utilize computing resources in the presence of constraints related to real time performance We first present a novel approach to rapid collision detection so as to maximize the available time for computing collision

Original URL path: http://www.scorec.rpi.edu/reports/view_report.php?id=313 (2015-07-15)

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techniques to improve the efficiency and accuracy of the precorrected FFT accelerated Fast Stokes solver based on a boundary element discretization of the integral form of the incompressible Stokes flow equations It is shown that a factor of three reduction of grid data storage may be achieved by deriving an alternative form of the Stokes kernels using second order derivatives of the distance function We propose two new techniques of

Original URL path: http://www.scorec.rpi.edu/reports/view_report.php?id=314 (2015-07-15)

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finite element method has emerged as a highly effective and successful numerical technique for the solution of a wide variety of boundary value problems in Engineering However in these techniques a great deal of effort is associated with the generation of a good quality mesh For this reason there is much interest in the development of so called meshless techniques The method of finite spheres 1 was introduced as a truly meshless technique with the goal of achieving computational efficiency In the method of finite spheres interpolation is performed using functions that are compactly supported on n dimensional spheres n 1 2 or 3 which form a covering for the analysis domain It was observed that for incompressible or nearly incompressible media the pure displacement based formulation exhibits a degradation of accuracy and convergence rate This phenomenon is known as volumetric locking In order to remedy the problem of locking we present a mixed formulation based on displacement and pressure interpolations However unlike a pure displacement based formulation a displacement pressure mixed formulation may behave reasonably for certain problems and completely fail for certain others unless the displacement and pressure approximation spaces are properly chosen To obtain a stable and

Original URL path: http://www.scorec.rpi.edu/reports/view_report.php?id=315 (2015-07-15)

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technique with the goal of achieving computational efficiency In the method of finite spheres discretization is performed using low cost partition of unity functions that are compactly supported on n dimensional spheres Dirichlet boundary conditions are imposed efficiently and the numerical integration of the terms in the Galerkin weak form is performed using specialized numerical integration rules Unlike in the traditional finite element methods the integrands in the method of finite spheres are rational functions the integration domains are general spheres or spheres truncated by the domain boundary or general lens shaped regions of overlap of two spheres Hence the development of efficient numerical integration schemes for the terms in the weak form without using a mesh is the key to achieving computational efficiency in the method of finite spheres We have developed a set of numerical integration rules on disks sectors and the lens shaped regions of overlap of two disks which result in a significant improvement in computational efficiency The automatic placement of nodal points the choice of the radii of the spheres for optimal accuracy and such other implementational issues are also important in deciding the overall efficiency of our computational scheme In this paper we present

Original URL path: http://www.scorec.rpi.edu/reports/view_report.php?id=316 (2015-07-15)

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make the automatic generation of a good quality mesh a nontrivial task especially in three dimensions To alleviate this problem we introduced the method of finite spheres De and Bathe 2001 as a generalization of the traditional finite element technique In the finite element technique the mesh is generated to define the shape functions which are piece wise Lagrange polynomials The support of the shape function defined at a node corresponds to the union of the elements that contain the node This results in a banded stiffness matrix with desirable properties However since the support is an n dimensional polytope certain element shapes should not be used namely those for which Jacobians are singular or almost singular or the accuracy of analysis is inadequate Bathe 1996 In the method of finite spheres the discretization is performed using functions that are compactly supported on n dimensional spheres The compact support of the functions results in banded stiffness matrices just as in the finite element method However since the supports of the shape functions are regular the element Jacobians are well behaved The only important criterion is that the spheres cover the entire domain Therefore generating an acceptable nodal arrangement in the method of finite spheres is not as difficult as generating a good quality mesh for a traditional finite element analysis This is a definite advantage for the analysis of many problems in the linear and nonlinear analysis of solids and structures and the analysis of fluid structure systems The method of finite spheres may be viewed as a generalized finite element technique in which the spheres behave conceptually as finite elements However unlike the traditional finite elements the spheres are not constrained to abut each other In the traditional finite element technique we are used to employ Galerkin formulations and

Original URL path: http://www.scorec.rpi.edu/reports/view_report.php?id=317 (2015-07-15)

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applications towards the use with ADINA and a surgical simulator Year 2002 Journal Computational Mechanics Volume 31 Pages 27 37 Abstract In this paper we report the development of a geometry based automatic prepocessing environment for the method of finite spheres a truly meshfree numerical technique developed for the solution of boundary value problems on geometrically complex domains Techniques of generating open covers for the Galerkin based as well as

Original URL path: http://www.scorec.rpi.edu/reports/view_report.php?id=318 (2015-07-15)

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Technique with an Orthogonal Basis Applied to Compressible Flow Problems Year 2002 Journal SIAM Journal on Scientific Computing Volume in press Pages 20 Abstract We present a high order formulation for solving hyperbolic conservation laws using the Discontinuous Galerkin Method DGM We introduce an orthogonal basis for the spatial discretization and use explicit Runge Kutta time discretization Some results of higher order adaptive re nement calculations are presented for inviscid

Original URL path: http://www.scorec.rpi.edu/reports/view_report.php?id=319 (2015-07-15)

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