ME964High Performance Computing for Engineering Applications“The first 90 percent of the code accounts for the first 90 percent of the development time. The remaining 10 percent of the code accounts for the other 90 percent of the development time.”—Tom Cargill© Dan Negrut, 2011ME964 UW-MadisonOverview of ME964 Final ProjectsApril 14, 2011Before We Get Started… Last Time  Parallel programming patterns One slide summary of ME964 Today Quickly go through your Final Project proposal presentations Other issues: Assignment 8 (last ME964 assignment) due today at 11:59 PM Midterm exam on April 19 Review session the evening before Syllabus called for closed books, it’s ok to bring whatever source of information you want with you From now on only guest lectures and such, time to concentrate on your projects IMPORTANT: Final Project Proposal PDF doc due on Tu, at 11:59 PM You submitted a proposal and/or provided a 3 slide presentation on the topic of your choice If you don’t hear back from me it means that I’m ok with the topic you proposed and you should get going on your Final Project I will use Doodle to allow you to enter the time/day when you choose to present your Final Project work2Discretized Poisson Sparse Matrix Solver with Conjugate Gradient MethodSpring 2011Lakshman AnumoluDepartment of Mechanical EngineeringUniversity of Wisconsin, MadisonMotivation & Illustration Fluid flow simulations require the solution of Poisson equation. Solving Poisson equation is computationally expensive for high fidelity simulations. Discretized Poisson matrix contains at most 5 non-zero elements in each row.(Example: For 5x5 nodes with known boundary conditions)1[1]http://en.wikipedia.org/wiki/Discrete_Poisson_equation#Example4Goal Midterm project: Implementation of Conjugate Gradient method for solving above system on GPU. Final project: Extending above implementation by modifying the method to use symmetric nature of discretized matrix. Comparing the performance with sparse matrix solver “SpeedIT_classic2”.[2] http://speedit.vratis.com/5Isotropic Projection Gridding for MRI ApplicationsMike LoecherProblem: Grid 3D radial data onto a Cartesian grid so that an FFT can be performed to obtain our final image• Gridding is the biggest time sink in the full image reconstruction• Large data sets (~10,000,000 points per image x multiple timeframes)• Potential to get a full reconstruction to a doctor while the patient is still in the scanner• Some prior work by another author showed a speedup of around 100x, but in 2D and with a different trajectoryReasoning and prior work7• Implement gridding for 3D isotropic projection data• Obtain images with very little error compared to CPU gridding• Optimize handling of variable sampling density (probably by separating into dense and sparse regions and handling differently)Outcomes8Modeling the effects of applied stresses on granular materials with the discrete element methodIan C. OlsonCurrent GPU DEM code:knNew GPU DEM code: Ff•Normal Stiffness Kn•Fixed boundaries•Fixed particle size•Add particle friction Ff•Add capacity for variability in particle size•Fixed, smooth side boundaries•Smooth top / bottom boundaries apply stress to highest / lowest particles•Output force distribution in system•Automated variation in σ when system reaches equilibrium•Output changes in system height h with corresponding applied stressσσh9TJ Colgan – ECE Department Final Project Problem Statement Develop GPU friendly code to compute a preconditioner used in the finite element analysis of thin structures.10GPU Friendly Preconditioners Why? Many research projects, including my own, involve the solution of a linear system that is either impractical or impossible to solve directly. Using a preconditioner in iterative solvers can greatly reduce computation time and the number of iterations to solve the system but they are not easily implemented on a GPU. Preliminary Results Dr. Suresh has already developed parts of the CUDA code and theory to implement a preconditioner on a GPU, as well as Abhirami and I have already implemented the calculation of the general metric over a triangular mesh and are validating and investigating the accuracy of our code.11GPU Friendly Preconditioners Deliverables CUDA C code to complete the following tasks Accurately calculate the general metric over the elements of a 3D triangular mesh Calculate the general metric of a 3D structure for the volume inside of a bounding box Calculate the stiffness matrix of a 3D structure using a general metric formulation12ME964Final ProjectBrian J. DavisMedical Physics/BMEFinal Project Brian J. Davis Medical Physics / BME Conebeam Backprojection Reconstruction for C-Arm CT and associated algorithms Need for real time cone-beam backprojections of projection images for four dimensional digital subtraction angiography (4D DSA) Example of C-Arm CT - Siemens Artis Zeego shown14Rational Need for real-time assessment of the health and assessment of disease of a vascular network of a patient. Allow for 4D (3D time resolved volumes) to be viewed and rotated to any angle by the Radiologist  Allow selection of Region of Interest (ROI) to be selected showing perfusion, pulse, and Time of Arrival by the Radiologist.15Summary of Outcomes (Deliverables) Decrease backprojection reconstruction by the greatest degree possible. Current 512x512x397 reconstruction ~10 min on Tesla c1060. Matlab version was 2.5 days. Goal < 1 minute. Port other stages of recon to GPU currently in MATLAB with Mex interface. Log subtract, Parker Weights, Cosine Weighting, 4D-DSA, Time Interval Difference (TID), Color mapping, rendering (VTK), etc. Forward Projection (time allotting) – Reverse of back projection. Requires solving a sparse matrix of a linear system of equations.16ME 964Kwang Won Choi The correlation between two signals (cross correlation) is a typical approach to feature detection.  The basic idea of this algorithm is finding the correlation coefficient between template feature (also called kernel) and input images18 The normalized cross-correlation between two signals of length N is defined as: The result is that rxyapproaches 1 only when the region of image contained the template. 19 Elastography in the field of bio-research is a