1. Quality of Service for Numerical Components Lori Freitag Diachin, Paul Hovland, Kate Keahey, Lois McInnes, Boyana Norris, Padma Raghavan

2. Motivation  Application developers should be able to achieve high performance and reliable implementation using components.  Components with identical interfaces and semantics may have different quality-of- service properties.

3. Goal and Scope  Goal: support QoS-driven component selection at composition time and runtime.  What are the motivating scenarios?  How to specify QoS metrics? –Once metrics have been identified and catalogued, define protocols for use.  Brokering: how to match up QoS clients and servers? –How to negotiate and compose components that are compatible? What interfaces are needed?  What algorithms (composite, adaptive) can take advantage of components with different QoS attributes, i.e., who are the QoS clients?

4. Motivation  Simulations in various areas, such as fusion, astrophysics, and computational fluid dynamics, consist of multiple numerical components, e.g. –Mesh management –Discretization –Derivative computation –Solution of linear and nonlinear systems of equations

5. Motivating Simulation Scenarios  PDE-based applications, for example –modeling flow over an airfoil Far field domain may not require full fidelity to the physical processes: a less accurate mathematical model may be employed or a low-order discretization technique Near the airfoil much higher fidelity and resolution may be required –driven cavity flow Pseudo-transient continuation method: solving a nonlinear system at each time step; Linear systems are initially well-conditioned, becoming more challenging as the pseudo time step grows

6. Motivating Scenarios (cont.) finite difference mesh (structured) finite element mesh (unstructured) finite volume mesh (unstructured) finite element discretization PPM discretization spectral mesh (largely hexahedral) fixed (not adaptive) h-adaptivity r-adaptivity low/high order discretization MeshDiscretizationAdaptivity p-adaptivity

7. Motivating Scenarios (cont.) Newton-Krylov Nonlinear Solver linear solver Alinear solver Blinear solver C desired properties offered and delivered properties function evaluation A line search function evaluation B Jacobian evaluation A Jacobian evaluation B monitor

8. linear solver Alinear solver Blinear solver C Component Substitution Set linear solver proxy: solve f’(u) du = -f(u) component monitoring Newton-Krylov solver application monitoring Newton solver (and linear solver proxy) request: || r ||/|| r 0 || < ε in k max iters application driver Initial runs achieved: linear solver A: || r ||/|| r 0 || <.0001 in average 42 Krylov iters linear solver B: || r ||/|| r 0 || <.0001 in average 30 Krylov iters linear solver C: || r ||/|| r 0 || <.0001 in average 14 Krylov iters application requests: || f ||/|| f 0 || < δ analysis, optimization, replacement, and substitution decision services: If the Newton method is not making sufficient nonlinear convergence progress,then switch to a more robust linear solver method, e.g., If || f ||/|| f 0 || < δ over n nonlinear iterations and || r ||/|| r 0 || < ε in k max Krylov iterations, then keep the same linear solver; otherwise switch. – Vertex – Forward edge – Backward edge Example

9. Metrics  Computational cost – based on static models or use as stopping criteria –wall-clock time, CPU time, FLOPs, iterations –parallel performance degradation (models)  Accuracy –residual norms (absolute, relative); asymptotic discretization error; truncation error (e.g. in finite difference approximations)  Failure rate  Convergence rate  Preconditioner quality –amount of fill of an incomplete factorization relative to a complete factorization given a particular ordering  Mesh quality  Function smoothness,  Etc…

10. Collaborations  Leverage: –Active Harmony (PERC) –Performance observation components (CCTTSS/TAU) –Performance assertions (PERC) –Performance models (PERC & others) –QoS metrics (PERC, TOPS, TSTT, CCTTSS, …) –Other research  QoS in both SPMD and distributed environments  Applications in which to apply and test the evolving QoS infrastructure implementation