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VITRTUS
CFD OF THE BLOOD FLOW IN THE CLOUD
JAKUB POLA
SOFTWARE DEVELOPER, VRATIS LTD.
HEART DIAGNOSIS
 Non-invasive:
‒ X-Ray Computer Tomography.
‒ Magnetic Resonance Imaging.
‒ Electrocardiography.

 Invasive:
‒ Angiography.
‒ Fractional Flow Reserve.

2 | PRESENTATION TITLE | NOVEMBER 14, 2013 | CONFIDENTIAL
HEART DIAGNOSIS
FRACTIONAL FLOW RESERVE EXAMPLE

 COURAGE, FAME2:
FFR VALUE

Stent
implantation

Drug
therapy

 DeFACTO (2012):

FFR
3 | PRESENTATION TITLE | NOVEMBER 14, 2013 | CONFIDENTIAL

FFR CT
COMPUTATIONAL FLUID DYNAMICS
FRAMEWORK

 Solve Navier – Stokes equations
 Procedure:
‒ Preprocessing:
‒
‒
‒
‒

Definition of the geometry.
Generation of volumetric mesh.
Definition of physical model.
Definition of boundary conditions.

‒ Simulation: iterative solvers.
‒ Post-processing:
‒ Analysis
‒ Visualisation

 How to obtain geometry and create a mesh?
 How to solve the problem fast and efficiently?
4 | PRESENTATION TITLE | NOVEMBER 14, 2013 | CONFIDENTIAL
CFD IN MEDICINE
 Stent graft design:
‒ Determination of proper shape of the stent graft

 Design of heart valves:
‒ Determination of shape and biological and mechanical
properties

 Drug delivery:
‒ Determination of the delivery device
‒ Determination of the drug state

5 | PRESENTATION TITLE | NOVEMBER 14, 2013 | CONFIDENTIAL
VIRTUS: OVERVIEW
Mesh storage format

User Interface

Database

PACS
Software as a Service

Active Mesh

6 | PRESENTATION TITLE | NOVEMBER 14, 2013 | CONFIDENTIAL

Calculations
VIRTUS: WORKFLOW

CT / MRI Scanning

Segmentation

CFD Simulation
7 | PRESENTATION TITLE | NOVEMBER 14, 2013 | CONFIDENTIAL

Meshing

Post-processing / Visualisation
VIRTUS: ARCHITECTURE

STL

Segmentation
CT/MRI

V Mesh

Surface representation of
volumetric mesh

Simulation

4 txt config files

Set boundary conditions

Visualization

8 | PRESENTATION TITLE | NOVEMBER 14, 2013 | CONFIDENTIAL

Generation of Volumetric
Mesh
(NETGEN)

surface & U, p, WSS

Simulation
VIRTUS: GRAPHIC USER INTERFACE

9 | PRESENTATION TITLE | NOVEMBER 14, 2013 | CONFIDENTIAL
VIRTUS: ARCHITECTURE

STL

Segmentation
CT/MRI

V Mesh

Surface representation of
volumetric mesh

Simulation

4 txt config files

Set boundary conditions

Visualization

10 | PRESENTATION TITLE | NOVEMBER 14, 2013 | CONFIDENTIAL

Generation of Volumetric
Mesh
(NETGEN)

surface & U, p, WSS

Simulation
VIRTUS: SEGMENTATION
 Create 3D model from series of images.
 Very time consuming task.
 Require mesh modeling to:
‒ fix the errors in the mesh
‒ prepare mesh to generate volumetric mesh

11 | PRESENTATION TITLE | NOVEMBER 14, 2013 | CONFIDENTIAL
VIRTUS: SEGMENTATION
ACTIVE MESH

 Input:
‒ CT or MRI scans in DICOM format.

 Outputs:
‒ Surface mesh in STL format.
‒ Volumetric mesh in OpenFOAM format.

 Real-time procedure.
 Fasat algorithm.
 Many mesh editing tools:
‒ Global/local mesh smoothing.
‒ Cut Mesh.
‒ Freeze Mesh.
‒ Push Mesh.
‒ Define Flow Inlets and Outlets
‒ Automated determination of artery centerline(s)
12 | PRESENTATION TITLE | NOVEMBER 14, 2013 | CONFIDENTIAL
VIRTUS: MESHING MODULE

13 | PRESENTATION TITLE | NOVEMBER 14, 2013 | CONFIDENTIAL
VIRTUS: ARCHITECTURE

STL

Segmentation
CT/MRI

V Mesh

Surface representation of
volumetric mesh

Simulation

4 txt config files

Set boundary conditions

Visualization

14 | PRESENTATION TITLE | NOVEMBER 14, 2013 | CONFIDENTIAL

Generation of Volumetric
Mesh
(NETGEN)

surface & U, p, WSS

Simulation
VIRTUS: SIMULATION MODULE
USER SIDE

 Just two steps:
‒ Type of simulation:
‒ Transient flows.
‒ Steady-state flows.

‒ Inlet boundary condition:
‒ Inlet velocity.
‒ Inlet pressure.
‒ Point and click procedure

 Configuration
‒ Just four txt files

15 | PRESENTATION TITLE | NOVEMBER 14, 2013 | CONFIDENTIAL
VIRTUS: SIMULATION MODULE
USER SIDE

16 | PRESENTATION TITLE | NOVEMBER 14, 2013 | CONFIDENTIAL
VIRTUS: SIMULATION MODULE
SERVER SIDE

 Three ways to execute simulation:
‒ Using CPU in parallel mode.
‒ Using CPU + GPU in parallel mode.
‒ Using GPU only.

17 | PRESENTATION TITLE | NOVEMBER 14, 2013 | CONFIDENTIAL
VIRTUS: SIMULATION MODULE
SERVER SIDE: CPU

CPU
Read mesh

Assembly matrices
Ax=b
~33%
No
Conv
erged
?

Yes
Finalize

18 | PRESENTATION TITLE | NOVEMBER 14, 2013 | CONFIDENTIAL

Solve
Ax=b

~66%
VIRTUS: SIMULATION MODULE
SERVER SIDE: CPU + GPU

CPU

PCI

GPU

Read mesh

Assembly matrices
Ax=b

No

Conv
erged
?

Yes
Finalize

19 | PRESENTATION TITLE | NOVEMBER 14, 2013 | CONFIDENTIAL

Ax=b

x

Solve
Ax=b
VIRTUS: SPEEDIT TOOLKIT
 Solvers:
‒ Conjugate Gradient.
‒ Bi-Conjugate Gradient.

 Preconditioners:
‒ Diagonal.
‒ Approximate Inverse.
‒ Algebraic Multigrid with Smoothed
Aggregation (CUSP).

 Support for Multi-GPU.
 Platforms:
‒ OpenCL.
‒ CUDA.

20 | PRESENTATION TITLE | NOVEMBER 14, 2013 | CONFIDENTIAL
VIRTUS: SIMULATION MODULE
SERVER SIDE: CPU + GPU

CPU

PCI

GPU

Read mesh

Assembly matrices
Ax=b

No

Conv
erged
?

Yes
Finalize

21 | PRESENTATION TITLE | NOVEMBER 14, 2013 | CONFIDENTIAL

Ax=b

x

Solve
Ax=b
VIRTUS: SIMULATION MODULE
SERVER SIDE: GPU

CPU
Read mesh

PCI

GPU

Mesh
Assembly matrices
Ax=b

No

Finalize

22 | PRESENTATION TITLE | NOVEMBER 14, 2013 | CONFIDENTIAL

x

Solve
Ax=b

Conv
erged
?

Yes
VIRTUS: SPEEDIT FLOW
 Full GPU implementation of:
‒ PISO (Pressure Implicit with Split Operator) – transient solver for incompressible flows.
‒ SIMPLE (Semi-implicit Method for Pressure Linked Equations): Steady-state solver for incompressible
flows.

 Boundary Conditions:
‒ Zero Gradient
‒ Time dependent and Fixed value.

 Adjustable time step.
 Roadmap:
‒ Support for OpenCL
‒ Turbulence (RANS, kOmegaSST model)
‒ Support for Multi-GPU
23 | PRESENTATION TITLE | NOVEMBER 14, 2013 | CONFIDENTIAL
SPEEDIT FLOW
TEST CASES

 U-shaped pipe
‒ Radius – 1in
‒ 4M hex cells
‒ Transient flow simulation:
‒ U(t) = Asin(ωt) + B

‒ Steady-state simulation
‒ Re = 100
‒ Re = 1000

 Basilar artery*:
‒ 2M hex cells
‒ Transient flow.
‒ Two heart cycles.

* Geometry obtained from AneuriskWeb project. Emory University, Department of Math&CS, 2012
24 | PRESENTATION TITLE | NOVEMBER 14, 2013 | CONFIDENTIAL
SPEEDIT FLOW: U-SHAPED PIPE
SIMULATION EXECUTION TIME

25 | PRESENTATION TITLE | NOVEMBER 14, 2013 | CONFIDENTIAL
SPEEDIT FLOW: U-SHAPED PIPE
ACCELERATION RATIO

26 | PRESENTATION TITLE | NOVEMBER 14, 2013 | CONFIDENTIAL
SPEEDIT FLOW: BASILAR ARTERY
SIMULATION EXECUTION TIME

27 | PRESENTATION TITLE | NOVEMBER 14, 2013 | CONFIDENTIAL
SPEEDIT FLOW: BASILAR ARTERY
ACCELERATION RATIO

28 | PRESENTATION TITLE | NOVEMBER 14, 2013 | CONFIDENTIAL
VIRTUS: ARCHITECTURE

STL

Segmentation
CT/MRI

V Mesh

Surface representation of
volumetric mesh

Simulation

4 txt config files

Set boundary conditions

Visualization

29 | PRESENTATION TITLE | NOVEMBER 14, 2013 | CONFIDENTIAL

Generation of Volumetric
Mesh
(NETGEN)

surface & U, p, WSS

Simulation
VRATIS: VISUALIZATION MODULE

30 | PRESENTATION TITLE | NOVEMBER 14, 2013 | CONFIDENTIAL
SUMMARY
 VIRTUS is a platform for personalized medicine and CFD based diagnosis.

 Cloud-based approach simplifies the usage.

 GPU reduces time-to-solution.

31 | PRESENTATION TITLE | NOVEMBER 14, 2013 | CONFIDENTIAL
Questions?
Comments?
Jakub Pola
jakub.pola@vratis.com
virtus.vratis.com
Acknowledemnents:
Vratis: Wojciech Tarnawski, Lukasz Miroslaw, Pawel Czubinski
Wroclaw Uni.: Zbigniew Koza, Piotr Olkiewicz
Wroclaw Uni. of Technology: Tadeusz Tomczak, Andrzej Kosior

32 | PRESENTATION TITLE | NOVEMBER 14, 2013 | CONFIDENTIAL
DISCLAIMER & ATTRIBUTION

The information presented in this document is for informational purposes only and may contain technical inaccuracies, omissions and typographical errors.
The information contained herein is subject to change and may be rendered inaccurate for many reasons, including but not limited to product and roadmap
changes, component and motherboard version changes, new model and/or product releases, product differences between differing manufacturers, software
changes, BIOS flashes, firmware upgrades, or the like. AMD assumes no obligation to update or otherwise correct or revise this information. However, AMD
reserves the right to revise this information and to make changes from time to time to the content hereof without obligation of AMD to notify any person of
such revisions or changes.
AMD MAKES NO REPRESENTATIONS OR WARRANTIES WITH RESPECT TO THE CONTENTS HEREOF AND ASSUMES NO RESPONSIBILITY FOR ANY
INACCURACIES, ERRORS OR OMISSIONS THAT MAY APPEAR IN THIS INFORMATION.
AMD SPECIFICALLY DISCLAIMS ANY IMPLIED WARRANTIES OF MERCHANTABILITY OR FITNESS FOR ANY PARTICULAR PURPOSE. IN NO EVENT WILL AMD BE
LIABLE TO ANY PERSON FOR ANY DIRECT, INDIRECT, SPECIAL OR OTHER CONSEQUENTIAL DAMAGES ARISING FROM THE USE OF ANY INFORMATION
CONTAINED HEREIN, EVEN IF AMD IS EXPRESSLY ADVISED OF THE POSSIBILITY OF SUCH DAMAGES.

ATTRIBUTION
© 2013 Advanced Micro Devices, Inc. All rights reserved. AMD, the AMD Arrow logo and combinations thereof are trademarks of Advanced Micro Devices,
Inc. in the United States and/or other jurisdictions. SPEC is a registered trademark of the Standard Performance Evaluation Corporation (SPEC). Other names
are for informational purposes only and may be trademarks of their respective owners.
33 | PRESENTATION TITLE | NOVEMBER 14, 2013 | CONFIDENTIAL

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Blood Flow Simulations in the Cloud

  • 1. VITRTUS CFD OF THE BLOOD FLOW IN THE CLOUD JAKUB POLA SOFTWARE DEVELOPER, VRATIS LTD.
  • 2. HEART DIAGNOSIS  Non-invasive: ‒ X-Ray Computer Tomography. ‒ Magnetic Resonance Imaging. ‒ Electrocardiography.  Invasive: ‒ Angiography. ‒ Fractional Flow Reserve. 2 | PRESENTATION TITLE | NOVEMBER 14, 2013 | CONFIDENTIAL
  • 3. HEART DIAGNOSIS FRACTIONAL FLOW RESERVE EXAMPLE  COURAGE, FAME2: FFR VALUE Stent implantation Drug therapy  DeFACTO (2012): FFR 3 | PRESENTATION TITLE | NOVEMBER 14, 2013 | CONFIDENTIAL FFR CT
  • 4. COMPUTATIONAL FLUID DYNAMICS FRAMEWORK  Solve Navier – Stokes equations  Procedure: ‒ Preprocessing: ‒ ‒ ‒ ‒ Definition of the geometry. Generation of volumetric mesh. Definition of physical model. Definition of boundary conditions. ‒ Simulation: iterative solvers. ‒ Post-processing: ‒ Analysis ‒ Visualisation  How to obtain geometry and create a mesh?  How to solve the problem fast and efficiently? 4 | PRESENTATION TITLE | NOVEMBER 14, 2013 | CONFIDENTIAL
  • 5. CFD IN MEDICINE  Stent graft design: ‒ Determination of proper shape of the stent graft  Design of heart valves: ‒ Determination of shape and biological and mechanical properties  Drug delivery: ‒ Determination of the delivery device ‒ Determination of the drug state 5 | PRESENTATION TITLE | NOVEMBER 14, 2013 | CONFIDENTIAL
  • 6. VIRTUS: OVERVIEW Mesh storage format User Interface Database PACS Software as a Service Active Mesh 6 | PRESENTATION TITLE | NOVEMBER 14, 2013 | CONFIDENTIAL Calculations
  • 7. VIRTUS: WORKFLOW CT / MRI Scanning Segmentation CFD Simulation 7 | PRESENTATION TITLE | NOVEMBER 14, 2013 | CONFIDENTIAL Meshing Post-processing / Visualisation
  • 8. VIRTUS: ARCHITECTURE STL Segmentation CT/MRI V Mesh Surface representation of volumetric mesh Simulation 4 txt config files Set boundary conditions Visualization 8 | PRESENTATION TITLE | NOVEMBER 14, 2013 | CONFIDENTIAL Generation of Volumetric Mesh (NETGEN) surface & U, p, WSS Simulation
  • 9. VIRTUS: GRAPHIC USER INTERFACE 9 | PRESENTATION TITLE | NOVEMBER 14, 2013 | CONFIDENTIAL
  • 10. VIRTUS: ARCHITECTURE STL Segmentation CT/MRI V Mesh Surface representation of volumetric mesh Simulation 4 txt config files Set boundary conditions Visualization 10 | PRESENTATION TITLE | NOVEMBER 14, 2013 | CONFIDENTIAL Generation of Volumetric Mesh (NETGEN) surface & U, p, WSS Simulation
  • 11. VIRTUS: SEGMENTATION  Create 3D model from series of images.  Very time consuming task.  Require mesh modeling to: ‒ fix the errors in the mesh ‒ prepare mesh to generate volumetric mesh 11 | PRESENTATION TITLE | NOVEMBER 14, 2013 | CONFIDENTIAL
  • 12. VIRTUS: SEGMENTATION ACTIVE MESH  Input: ‒ CT or MRI scans in DICOM format.  Outputs: ‒ Surface mesh in STL format. ‒ Volumetric mesh in OpenFOAM format.  Real-time procedure.  Fasat algorithm.  Many mesh editing tools: ‒ Global/local mesh smoothing. ‒ Cut Mesh. ‒ Freeze Mesh. ‒ Push Mesh. ‒ Define Flow Inlets and Outlets ‒ Automated determination of artery centerline(s) 12 | PRESENTATION TITLE | NOVEMBER 14, 2013 | CONFIDENTIAL
  • 13. VIRTUS: MESHING MODULE 13 | PRESENTATION TITLE | NOVEMBER 14, 2013 | CONFIDENTIAL
  • 14. VIRTUS: ARCHITECTURE STL Segmentation CT/MRI V Mesh Surface representation of volumetric mesh Simulation 4 txt config files Set boundary conditions Visualization 14 | PRESENTATION TITLE | NOVEMBER 14, 2013 | CONFIDENTIAL Generation of Volumetric Mesh (NETGEN) surface & U, p, WSS Simulation
  • 15. VIRTUS: SIMULATION MODULE USER SIDE  Just two steps: ‒ Type of simulation: ‒ Transient flows. ‒ Steady-state flows. ‒ Inlet boundary condition: ‒ Inlet velocity. ‒ Inlet pressure. ‒ Point and click procedure  Configuration ‒ Just four txt files 15 | PRESENTATION TITLE | NOVEMBER 14, 2013 | CONFIDENTIAL
  • 16. VIRTUS: SIMULATION MODULE USER SIDE 16 | PRESENTATION TITLE | NOVEMBER 14, 2013 | CONFIDENTIAL
  • 17. VIRTUS: SIMULATION MODULE SERVER SIDE  Three ways to execute simulation: ‒ Using CPU in parallel mode. ‒ Using CPU + GPU in parallel mode. ‒ Using GPU only. 17 | PRESENTATION TITLE | NOVEMBER 14, 2013 | CONFIDENTIAL
  • 18. VIRTUS: SIMULATION MODULE SERVER SIDE: CPU CPU Read mesh Assembly matrices Ax=b ~33% No Conv erged ? Yes Finalize 18 | PRESENTATION TITLE | NOVEMBER 14, 2013 | CONFIDENTIAL Solve Ax=b ~66%
  • 19. VIRTUS: SIMULATION MODULE SERVER SIDE: CPU + GPU CPU PCI GPU Read mesh Assembly matrices Ax=b No Conv erged ? Yes Finalize 19 | PRESENTATION TITLE | NOVEMBER 14, 2013 | CONFIDENTIAL Ax=b x Solve Ax=b
  • 20. VIRTUS: SPEEDIT TOOLKIT  Solvers: ‒ Conjugate Gradient. ‒ Bi-Conjugate Gradient.  Preconditioners: ‒ Diagonal. ‒ Approximate Inverse. ‒ Algebraic Multigrid with Smoothed Aggregation (CUSP).  Support for Multi-GPU.  Platforms: ‒ OpenCL. ‒ CUDA. 20 | PRESENTATION TITLE | NOVEMBER 14, 2013 | CONFIDENTIAL
  • 21. VIRTUS: SIMULATION MODULE SERVER SIDE: CPU + GPU CPU PCI GPU Read mesh Assembly matrices Ax=b No Conv erged ? Yes Finalize 21 | PRESENTATION TITLE | NOVEMBER 14, 2013 | CONFIDENTIAL Ax=b x Solve Ax=b
  • 22. VIRTUS: SIMULATION MODULE SERVER SIDE: GPU CPU Read mesh PCI GPU Mesh Assembly matrices Ax=b No Finalize 22 | PRESENTATION TITLE | NOVEMBER 14, 2013 | CONFIDENTIAL x Solve Ax=b Conv erged ? Yes
  • 23. VIRTUS: SPEEDIT FLOW  Full GPU implementation of: ‒ PISO (Pressure Implicit with Split Operator) – transient solver for incompressible flows. ‒ SIMPLE (Semi-implicit Method for Pressure Linked Equations): Steady-state solver for incompressible flows.  Boundary Conditions: ‒ Zero Gradient ‒ Time dependent and Fixed value.  Adjustable time step.  Roadmap: ‒ Support for OpenCL ‒ Turbulence (RANS, kOmegaSST model) ‒ Support for Multi-GPU 23 | PRESENTATION TITLE | NOVEMBER 14, 2013 | CONFIDENTIAL
  • 24. SPEEDIT FLOW TEST CASES  U-shaped pipe ‒ Radius – 1in ‒ 4M hex cells ‒ Transient flow simulation: ‒ U(t) = Asin(ωt) + B ‒ Steady-state simulation ‒ Re = 100 ‒ Re = 1000  Basilar artery*: ‒ 2M hex cells ‒ Transient flow. ‒ Two heart cycles. * Geometry obtained from AneuriskWeb project. Emory University, Department of Math&CS, 2012 24 | PRESENTATION TITLE | NOVEMBER 14, 2013 | CONFIDENTIAL
  • 25. SPEEDIT FLOW: U-SHAPED PIPE SIMULATION EXECUTION TIME 25 | PRESENTATION TITLE | NOVEMBER 14, 2013 | CONFIDENTIAL
  • 26. SPEEDIT FLOW: U-SHAPED PIPE ACCELERATION RATIO 26 | PRESENTATION TITLE | NOVEMBER 14, 2013 | CONFIDENTIAL
  • 27. SPEEDIT FLOW: BASILAR ARTERY SIMULATION EXECUTION TIME 27 | PRESENTATION TITLE | NOVEMBER 14, 2013 | CONFIDENTIAL
  • 28. SPEEDIT FLOW: BASILAR ARTERY ACCELERATION RATIO 28 | PRESENTATION TITLE | NOVEMBER 14, 2013 | CONFIDENTIAL
  • 29. VIRTUS: ARCHITECTURE STL Segmentation CT/MRI V Mesh Surface representation of volumetric mesh Simulation 4 txt config files Set boundary conditions Visualization 29 | PRESENTATION TITLE | NOVEMBER 14, 2013 | CONFIDENTIAL Generation of Volumetric Mesh (NETGEN) surface & U, p, WSS Simulation
  • 30. VRATIS: VISUALIZATION MODULE 30 | PRESENTATION TITLE | NOVEMBER 14, 2013 | CONFIDENTIAL
  • 31. SUMMARY  VIRTUS is a platform for personalized medicine and CFD based diagnosis.  Cloud-based approach simplifies the usage.  GPU reduces time-to-solution. 31 | PRESENTATION TITLE | NOVEMBER 14, 2013 | CONFIDENTIAL
  • 32. Questions? Comments? Jakub Pola jakub.pola@vratis.com virtus.vratis.com Acknowledemnents: Vratis: Wojciech Tarnawski, Lukasz Miroslaw, Pawel Czubinski Wroclaw Uni.: Zbigniew Koza, Piotr Olkiewicz Wroclaw Uni. of Technology: Tadeusz Tomczak, Andrzej Kosior 32 | PRESENTATION TITLE | NOVEMBER 14, 2013 | CONFIDENTIAL
  • 33. DISCLAIMER & ATTRIBUTION The information presented in this document is for informational purposes only and may contain technical inaccuracies, omissions and typographical errors. The information contained herein is subject to change and may be rendered inaccurate for many reasons, including but not limited to product and roadmap changes, component and motherboard version changes, new model and/or product releases, product differences between differing manufacturers, software changes, BIOS flashes, firmware upgrades, or the like. AMD assumes no obligation to update or otherwise correct or revise this information. However, AMD reserves the right to revise this information and to make changes from time to time to the content hereof without obligation of AMD to notify any person of such revisions or changes. AMD MAKES NO REPRESENTATIONS OR WARRANTIES WITH RESPECT TO THE CONTENTS HEREOF AND ASSUMES NO RESPONSIBILITY FOR ANY INACCURACIES, ERRORS OR OMISSIONS THAT MAY APPEAR IN THIS INFORMATION. AMD SPECIFICALLY DISCLAIMS ANY IMPLIED WARRANTIES OF MERCHANTABILITY OR FITNESS FOR ANY PARTICULAR PURPOSE. IN NO EVENT WILL AMD BE LIABLE TO ANY PERSON FOR ANY DIRECT, INDIRECT, SPECIAL OR OTHER CONSEQUENTIAL DAMAGES ARISING FROM THE USE OF ANY INFORMATION CONTAINED HEREIN, EVEN IF AMD IS EXPRESSLY ADVISED OF THE POSSIBILITY OF SUCH DAMAGES. ATTRIBUTION © 2013 Advanced Micro Devices, Inc. All rights reserved. AMD, the AMD Arrow logo and combinations thereof are trademarks of Advanced Micro Devices, Inc. in the United States and/or other jurisdictions. SPEC is a registered trademark of the Standard Performance Evaluation Corporation (SPEC). Other names are for informational purposes only and may be trademarks of their respective owners. 33 | PRESENTATION TITLE | NOVEMBER 14, 2013 | CONFIDENTIAL