Speedup linear

The lawn-mowing analogy is also interesting in that up to a certain point there will be a linear speedup as mowers are added. This speedup occurs because the mowers do not interfere with each other s work and have efficient mechanisms for coordinating their efforts. The lawn-mowing problem exhibits very good data paraHeHsm. 

The optimal eontrol profiles identified by the solution of the non-linear programme were used to simulate the network through rigorous distributed parameter models on SPEEDUP to obtain a detailed deseription of its... 

The first term is represents the motion of the lower left-hand comer and the second term, the linear expansion, indicates how the circumferential velocity changes over the length of the element, dr. Since the circumferential velocity w(r) is generally not a linear function of r, there is a relative speedup or slowdown of the right-hand comer relative to the linear rate, meaning that there is shearing as evidenced by da 0 and ds 0. The distance ds... 

Beste et al. [104] compared the results obtained with the SMB and the TMB models, using numerical solutions. All the models used assumed axially dispersed plug flow, the linear driving force model for the mass transfer kinetics, and non-linear competitive isotherms. The coupled partial differential equations of the SMB model were transformed with the method of lines [105] into a set of ordinary differential equations. This system of equations was solved with a conventional set of initial and boundary conditions, using the commercially available solver SPEEDUP. Eor the TMB model, the method of orthogonal collocation was used to transfer the differential equations and the boimdary conditions into a set of non-linear algebraic equations which were solved numerically with the Newton-Raphson algorithm. 

In this case, there is a fixed upper limit to the achievable speedup, and the efficiency decreases as the number of processors increases, regardless of the problem size. Thus, much work must be invested to achieve efficient parallelization of linear-scaling methods these methods involve a large number of steps that scale linearly in N, and each step must be parallelized to achieve high efficiency when running on large numbers of processors. 

By using a definition of /g that depends on p, Gustafson s law predicts a speedup without a fixed upper bound. Nofe, however, fhaf fhe speedup Sg (p) is nof a linear function of p, as it may appear from Eq. 5.11, because fc also depends on p. 

Speedup curves illustrating commonly encountered performance patterns, (a) ideal (b) superlinear speedup with performance degradation due to, e.g., communication overhead or load imbalance (c) logarithmic communication overhead (d) linear communication overhead (e) incompletely parallelized program (serial fraction of 0.025). See text for details. 

In order to extend these methods to make them feasible for the study dynamical chemical processes in biopolymers, simplifying assumptions are necessary. The most obvious choice is the use of semi-empirical techniques within the Hartree Fock, linear combination of atomic orbitals framework. These methods can achieve speedups on the order of 1000 over typical ab initio calculations using split valence basis sets within the Hartree Fock approximation. Often greater accuracy can be achieved as well because of the parameterization inherent in the semi-empirical approaches. One semi-empirical approach which has proven successful in representing many chemically interesting processes is the AMI and MNDO Hartree Fock Self-Consistent Field methods developed and paramerterized by Dewar and coworkers [46]. These methods have recently been implemented in a mixed quantum/ classical methodology for the study of chemical and biochemical processes by Field et al. [47]. 

As it stands, nowadays the architectural advantage of supercomputers is due almost entirely to parallelism, i.e., many processors in a supercomputer are commonly involved in a single computational task. Ideally, the speedup that is achieved increases linearly with the number of processors that are contributing to such a computational task. Because of the time spent in the coordination of the processors, this linear increase in speed is seldomly observed. Nevertheless, parallelism enables us to tackle computational problems that would be simply unthought of without it. 

S. E. DeBolt, D. A. Pearlman, and P. A. Kollman,/. Comput. Chem., 15, 351 (1994). Free Energy Perturbation Calculations on Parallel Computers Demonstrations of Scalable Linear Speedup. 

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