DRUM Community: Computer Sciencehttp://hdl.handle.net/1903/22242014-04-20T23:39:34Z2014-04-20T23:39:34ZRecursive computation of spherical harmonic rotation coefficients of large degreeGumerov, Nail A.Duraiswami, Ramanihttp://hdl.handle.net/1903/150132014-03-31T02:30:30Z2014-03-28T00:00:00ZTitle: Recursive computation of spherical harmonic rotation coefficients of large degree
Authors: Gumerov, Nail A.; Duraiswami, Ramani
Abstract: Computation of the spherical harmonic rotation coefficients or elements
of Wigner's d-matrix is important in a number of quantum mechanics and
mathematical physics applications. Particularly, this is important for
the Fast Multipole Methods in three dimensions for the Helmholtz,
Laplace and related equations, if rotation-based decomposition of
translation operators are used. In these and related problems related to
representation of functions on a sphere via spherical harmonic
expansions computation of the rotation coefficients of large degree n
(of the order of thousands and more) may be necessary. Existing
algorithms for their computation, based on recursions, are usually
unstable, and do not extend to n. We develop a new recursion and study
its behavior for large degrees, via computational and asymptotic
analyses. Stability of this recursion was studied based on a novel
application of the Courant-Friedrichs-Lewy condition and the von Neumann
method for stability of finite-difference schemes for solution of PDEs.
A recursive algorithm of minimal complexity O(n^2) for degree n and
FFT-based algorithms of complexity O(n^2 log n) suitable for computation
of rotation coefficients of large degrees are proposed, studied
numerically, and cross-validated. It is shown that the latter algorithm
can be used for n <~ 10^3 in double precision, while the former
algorithm was tested for large n (up to 10^4 in our experiments) and
demonstrated better performance and accuracy compared to the FFT-based
algorithm.2014-03-28T00:00:00ZStudying Directory Access Patterns via Reuse Distance Analysis and Evaluating Their Impact on Multi-Level Directory CachesZhao, MinshuYeung, Donaldhttp://hdl.handle.net/1903/149722014-02-19T03:30:26Z2014-01-13T00:00:00ZTitle: Studying Directory Access Patterns via Reuse Distance Analysis and Evaluating Their Impact on Multi-Level Directory Caches
Authors: Zhao, Minshu; Yeung, Donald
Abstract: The trend for multicore CPUs is towards increasing core count. One of
the key limiters to scaling will be the on-chip directory cache. Our
work investigates moving portions of the directory away from the cores,
perhaps to off-chip DRAM, where ample capacity exists. While such
multi-level directory caches exhibit increased latency, several aspects
of directory accesses will shield CPU performance from the slower
directory, including low access frequency and latency hiding underneath
data accesses to main memory.
While multi-level directory caches have been studied previously, no work
has of yet comprehensively quantified the directory access patterns
themselves, making it difficult to understand multi-level behavior in
depth. This paper presents a framework based on multicore reuse
distance for studying directory cache access patterns. Using our
analysis framework, we show between 69-93% of directory entries are
looked up only once or twice during their liftimes in the directory
cache, and between 51-71% of dynamic directory accesses are latency
tolerant. Using cache simulations, we show a very small L1 directory
cache can service 80% of latency critical directory lookups. Although a
significant number of directory lookups and eviction notifications must
access the slower L2 directory cache, virtually all of these are latency
tolerant.2014-01-13T00:00:00ZA Block Preconditioner for an Exact Penalty Formulation for Stationary MHDPhillips, Edward G.Elman, Howard C.Cyr, Eric C.Shadid, John N.Pawlowski, Roger P.http://hdl.handle.net/1903/149702014-02-13T03:32:08Z2014-02-04T00:00:00ZTitle: A Block Preconditioner for an Exact Penalty Formulation for Stationary MHD
Authors: Phillips, Edward G.; Elman, Howard C.; Cyr, Eric C.; Shadid, John N.; Pawlowski, Roger P.
Abstract: The magnetohydrodynamics (MHD) equations are used to model the flow of electrically conducting fluids in such applications as liquid metals and plasmas. This system of non-self adjoint, nonlinear PDEs couples the Navier-Stokes equations for fluids and Maxwell's equations for electromagnetics. There has been recent interest in fully coupled solvers for the MHD system because they allow for fast steady-state solutions that do not require pseudo-time stepping. When the fully coupled system is discretized, the strong coupling can make the resulting algebraic systems difficult to solve, requiring effective preconditioning of iterative methods for efficiency. In this work, we consider a finite element discretization of an exact penalty formulation for the stationary MHD equations. This formulation has the benefit of implicitly enforcing the divergence free condition on the magnetic field without requiring a Lagrange multiplier. We consider extending block preconditioning techniques developed for the Navier-Stokes equations to the full MHD system. We analyze operators arising in block decompositions from a continuous perspective and apply arguments based on the existence of approximate commutators to develop new preconditioners that account for the physical coupling. This results in a family of parameterized block preconditioners for both Picard and Newton linearizations.
We develop an automated method for choosing the relevant parameters and demonstrate the robustness of these preconditioners for a range of the physical non-dimensional parameters and with respect to mesh refinement.2014-02-04T00:00:00ZRegulation of Systemic Risk Through Contributory Endogenous Agent-Based ModelingBristor, Aurorahttp://hdl.handle.net/1903/149562014-02-13T03:31:42Z2013-01-01T00:00:00ZTitle: Regulation of Systemic Risk Through Contributory Endogenous Agent-Based Modeling
Authors: Bristor, Aurora
Abstract: The Financial Stability Oversight Council (FSOC) was created to identify and respond to emerging threats to the stability of the United States financial system. The research arm of the FSOC, the Office of Financial Research (OFR), has begun to explore agent-based models (ABMs) for measuring the emergent threat of systemic risk. We propose an ABM-based regulatory structure that incentivizes the honest participation and data contribution of regulated firms while providing clarity into the actions of the firms as endogenous to the market and driving emergent behavior. We build this scheme onto an existing ABM of a single-asset market to examine whether the structure of the scheme could provide its own benefits to market stabilization. We find that without regulatory intervention, markets acting within this proposed structure experience fewer bankruptcies and lower leverage buildup while returning larger profits for the same amount of risk.2013-01-01T00:00:00Z