# Presentation: 160412

## Algorithms, Methods, and Libraries

**Computer Science & Enabling Technologies:**
**Algorithms, Methods, and Libraries**

## Goal: provide application teams with numerical tools for terascale simulation

**Topics were chosen after consulting with members of the application efforts**
**common needs were identified**
**opportunity to leverage existing work**** **
**We will work closely with application teams to****	**
**deploy existing technology for early impact**
**develop terascale methods for success**
**conduct longer term research for outyears**

## Solving the problem:what, how, and who cares?

**Meshing and discretization technology**
***defining the problem****** ***
**Scalable numerical algorithms**
***solving the problem****** ***
**Predictability and reliability of simulation results**
***assessing the quality of the solution****** ***
**Scientific Data Exploration**
**assimilating the results**

## We need automatic, scalable, parallel mesh generation capabilities

**We need automatic, scalable, parallel mesh generation capabilities**

**Mesh generation is usually most ****time-consuming part of simulation**
**man-months to generate mesh**
**tuned to specific resolution**
**existing software is serial**** **
**Terascale simulation requires ****a new paradigm**
**complex geometries with 1B cells**
**mesh-independent device definition**
**automatic parallel mesh generation**
**parallel mesh partitioning**

## Complex geometries require sophisticated gridding technologies

**Fully unstructured grids**
**use both hex and tet elements**
**obtain numerical mesh from CAD specification**** **
**Overlapping structured grids**
**independently grid different regions and “glue” together**
**sophisticated numerics for overlap & interface regions**** **
**Object-oriented code frameworks **

## AMR technology allows one to focus computational effort where it is needed

**AMR technology allows one to focus computational effort where it is needed**

**Adaptively refine grid in vicinity of interesting behavior**** **
**AMR successfully used in CFD for years**** **
**Code framework allows scientist to focus on the science, not the CS**

**2D shock front in a chamber**

## Scalable numerical algorithms

**Linear systems**** **
**Nonlinear systems**** **
**Differential equations**** **
**Mathematical optimization**** **
**Radiation transport**

## Scalable numerical algorithms enable  terascale scientific simulation

**Goal: time-to-solution is constant as problem size increases with machine size**** **
**Algorithmic scalability is *****independent***** of parallel scalability**** **
**an iterative method is scalable if the number of iterations required for convergence is indpt of problem size**** **

***example:*****Scalability of Linear Solvers**

## Linear solvers are (still) a key computational kernel 

**Solution of large linear system is computational bottleneck in implicit codes**
**symmetric and nonsymmetric matrices**
**structured and unstructured meshes**** **
**Most simulation codes need sparse solvers**
**preconditioned Krylov methods**
**incomplete factorizations**
**sparse approximate inverse methods**
**multilevel methods**** **
**Some need for dense system solvers**

## Multigrid methods can be scalable and 10-1000 times faster than other solvers

**Geometric multigrid for structured grids**** **
**Algebraic multigrid for unstructured grids**** **
**Strongly varying coefficient functions**** **
**Multigrid solvers tend to be highly problem dependent**

***Need: efficient MG solver for AMR grid hierarchy****** ***
***Research issue: devise robust ******cell-based****** MG ****** ***

## Non-linear methods research, development and deployment  

**Newton-Krylov methods for nonlinear equations**** **
**Stiff ODEs and DAEs arise in many SSP applications**** **
**Mathematical optimization**
**quality software**
**multidisciplinary design optimization**** **
**Radiation transport**
**critical to many SSP and ASCI applications**
**ASCI burn code review: scalable transport now!**

## We need to develop methodologies to assess predictive quality of simulations

**Example: multiscale atmospheric modeling**
**predictability of regional climate variation **
**frequency of extreme events in altered climate**
**predictability of global climate change**** **
**Enhance predictability**
**simulation ensembles**
**stochastic approach**
**sensitivity analysis**

**Atmospheric processes ****span a wide range of scales**

## Uncertainty enters at each step of the simulation of complex phenomena

**Verification *****accurate numerical methods******analytic test problems***

**Validation*****comparison with experiments******sensitivity analysis***

**Execution *****terascale computing power******scalable numerical methods***

***How can we quantify the error in the output as a function of the input errors?***

## Sensitivity analysis gives us a way to quantify and understand uncertainty

**Quantify output variability as function of inputs**
**determine the most important input parameters**
**identify where more or better data is needed**
**guide experimental program**
**automation via optimization techniques**** **
**Identification of most important physical processes**
**model reduction without loss of relevant features**
**allows one to focus effort elsewhere**** **
**Develop parallel ODE/DAE sensitivity analysis solvers**
**we can leverage existing software**
**work with app teams to develop capability**

## We will propagate R&D results via high-quality mathematical software

**Mathematical software libraries allow research results  to be leveraged across many applications**
**easier maintenance**
**insertion path for new technology**** **
**Componentware-based design **
**insure interoperability of SSP math software**
**leverage DOE2000 CCA activity**
***a priori***** design versus *****a posteriori***** kludge**** **
**Explore new ideas in library development**
**automatic performance tuning of kernels**
**intelligent agents choose appropriate software**

## Our algorithms research and software development is applications-driven

**Research results are leveraged via reusable and interoperable software modules**

**DOE mission needs ****drive CSET algorithms ****R&D**

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Each research thrust area is motivated by the needs of a Laboratory program
We develop a general solution capability that can be leveraged over several applications
We develop common software frameworks and plug-and-play modules
We work with our collaborators to customize the solution to the motivating application and to integrate it into the application code

## CS&ET experts will team with application groups to insure relevance of research

**CS&ET experts will team with application groups to insure relevance of research**

***This committed teaming arrangement is the key to our success***

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