The current trends in computer architecture are shifting towards smaller byte/flop ratios, while available parallelism is increasing at all levels of granularity – vector length, core count, and MPI process. Intel’s Xeon Phi coprocessor, NVIDIA’s Kepler GPU, and IBM’s BlueGene/Q all have a Byte/flop ratio close to 0.2, which makes it very difficult for most algorithms to extract a high percentage of the theoretical peak flop/s from these architectures. Popular algorithms in scientific computing such as FFT are continuously evolving to keep up with this trend in hardware. In the meantime it is also necessary to invest in novel algorithms that are more suitable for computer architectures of the future. The fast multipole method (FMM) was originally developed as a fast algorithm for ap- proximating the N-body interactions that appear in astrophysics, molecular dynamics, and vortex based fluid dynamics simulations. The FMM possesses have a unique combination of being an efficient O(N) algorithm, while having an operational intensity that is higher than a matrix-matrix multiplication. In fact, the FMM can reduce the requirement of Byte/flop to around 0.01, which means that it will remain compute bound until 2020 even if the cur- rent trend in microprocessors continues. Despite these advantages, there have not been any benchmarks of FMM codes on modern architectures such as Xeon Phi, Kepler, and Blue- Gene/Q. This study aims to provide a comprehensive benchmark of a state of the art FMM code “exaFMM” on the latest architectures, in hopes of providing a useful reference for deciding when the FMM will become useful as the computational engine in a given application code. It may also serve as a warning to certain problem size domains areas where the FMM will exhibit insignificant performance improvements. Such issues depend strongly on the asymptotic constants rather than the asymptotics themselves, and therefore are strongly implementation and hardware dependent. The primary objective of this study is to provide these constants on various computer architectures.

Exascale systems are predicted to have approximately one billion cores, assuming Gigahertz cores. Limitations on affordable network topologies for distributed memory systems of such massive scale bring new challenges to the currently dominant parallel programing model. Currently, there are many efforts to evaluate the hardware and software bottlenecks of exascale designs. It is therefore of interest to model application performance and to understand what changes need to be made to ensure extrapolated scalability. Fast multipole methods (FMM) were originally developed for accelerating N-body problems for particle-based methods in astrophysics and molecular dynamics. FMM is more than an N-body solver, however. Recent efforts to view the FMM as an elliptic PDE solver have opened the possibility to use it as a preconditioner for even a broader range of applications. In this thesis, we (i) discuss the challenges for FMM on current parallel computers and future exascale architectures, with a focus on inter-node communication, and develop a performance model that considers the communication patterns of the FMM for spatially quasi-uniform distributions, (ii) employ this performance model to guide performance and scaling improvement of FMM for all-atom molecular dynamics simulations of uniformly distributed particles, and (iii) demonstrate that, beyond its traditional use as a solver in problems for which explicit free-space kernel representations are available, the FMM has applicability as a preconditioner in finite domain elliptic boundary value problems, by equipping it with boundary integral capability for satisfying conditions at finite boundaries and by wrapping it in a Krylov method for extensibility to more general operators. Compared with multilevel methods, FMM is capable of comparable algebraic convergence rates down to the truncation error of the discretized PDE, and it has superior multicore and distributed memory scalability properties on commodity architecture supercomputers. Compared with other methods exploiting the low rank character of off-diagonal blocks of the dense resolvent operator, FMM-preconditioned Krylov iteration may reduce the amount of communication because it is matrix-free and exploits the tree structure of FMM. Fast multipole-based solvers and preconditioners are demonstrably poised to play a leading role in exascale computing.

<p>The purpose of this dissertation is to present how online marketing tools influence customer relationship management (CRM) in a Business to Business (B to B) company. After reviewing the relevant theories, a frame of reference for client relations through the internet is selected from the research of Bauer</p><p><em>et al (2002). Six key characteristics of internet were discussed in order to reveal their impact on CRM. Meanwhile, three variables, which are commitment, satisfaction, and trust, are explored to measure the concept CRM. Both qualitative and quantitative research are used in this study, through analyzing the company’s internal documents, the authors come to a conclusion that the internet tool could improve customer satisfaction, commitment and trust, so as to improve customer relationship. <strong><p>Key words:</p><p>Internet marketing Tools, Customer Relationship Management, Commitment, Satisfaction, Trust, Webinar, Multiple method</p></strong></em></p>

The purpose of this dissertation is to present how online marketing tools influence customer relationship management (CRM) in a Business to Business (B to B) company. After reviewing the relevant theories, a frame of reference for client relations through the internet is selected from the research of Bauer et al (2002). Six key characteristics of internet were discussed in order to reveal their impact on CRM. Meanwhile, three variables, which are commitment, satisfaction, and trust, are explored to measure the concept CRM. Both qualitative and quantitative research are used in this study, through analyzing the company’s internal documents, the authors come to a conclusion that the internet tool could improve customer satisfaction, commitment and trust, so as to improve customer relationship. Key words: Internet marketing Tools, Customer Relationship Management, Commitment, Satisfaction, Trust, Webinar, Multiple method

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With the rapid increase in available compute power and memory, and bolstered by the advent of efficient formulations and algorithms, the role of 3D full-wave computational methods for accurate modelling of complex electromagnetic (EM) structures has gained in significance. The range of problems includes Radar Cross Section (RCS) computation, analysis and design of antennas and passive microwave circuits, bio-medical non-invasive detection and therapeutics, energy harvesting etc. Further, with the rapid advances in technology trends like System-in-Package (SiP) and System-on-Chip (SoC), the fidelity of chip-to-chip communication and package-board electrical performance parameters like signal integrity (SI), power integrity (PI), electromagnetic interference (EMI) are becoming increasingly critical. Rising pin-counts to satisfy functionality requirements and decreasing layer-counts to maintain cost-effectiveness necessitates 3D full wave electromagnetic solution for accurate system modelling. Method of Moments (MoM) is one such widely used computational technique to solve a 3D electromagnetic problem with full-wave accuracy. Due to lesser number of mesh elements or discretization on the geometry, MoM has an advantage of a smaller matrix size. However, due to Green's Function interactions, the MoM matrix is dense and its solution presents a time and memory challenge. The thesis focuses on formulation and development of novel techniques that aid in fast MoM based electromagnetic solutions. With the recent paradigm shift in computer hardware architectures transitioning from single-core microprocessors to multi-core systems, it is of prime importance to parallelize the serial electromagnetic formulations in order to leverage maximum computational benefits. Therefore, the thesis explores the possibilities to expedite an electromagnetic simulation by scalable parallelization of near-linear complexity algorithms like Fast Multipole Method (FMM) on a multi-core platform. Secondly, with the best of parallelization strategies in place and near-linear complexity algorithms in use, the solution time of a complex EM problem can still be exceedingly large due to over-meshing of the geometry to achieve a desired level of accuracy. Hence, the thesis focuses on judicious placement of mesh elements on the geometry to capture the physics of the problem without compromising on accuracy- a technique called Adaptive Mesh Refinement. This facilitates a reduction in the number of solution variables or degrees of freedom in the system and hence the solution time. For multi-scale structures as encountered in chip-package-board systems, the MoM formulation breaks down for parts of the geometry having dimensions much smaller as compared to the operating wavelength. This phenomenon is popularly known as low-frequency breakdown or low-frequency instability. It results in an ill-conditioned MoM system matrix, and hence higher iteration count to converge when solved using an iterative solver framework. This consequently increases the solution time of simulation. The thesis thus proposes novel formulations to improve the spectral properties of the system matrix for real-world complex conductor and dielectric structures and hence form well-conditioned systems. This reduces the iteration count considerably for convergence and thus results in faster solution. Finally, minor changes in the geometrical design layouts can adversely affect the time-to-market of a commodity or a product. This is because the intermediate design variants, in spite of having similarities between them are treated as separate entities and therefore have to follow the conventional model-mesh-solve workflow for their analysis. This is a missed opportunity especially for design variant problems involving near-identical characteristics when the information from the previous design variant could have been used to expedite the simulation of the present design iteration. A similar problem occurs in the broadband simulation of an electromagnetic structure. The solution at a particular frequency can be expedited manifold if the matrix information from a frequency in its neighbourhood is used, provided the electrical characteristics remain nearly similar. The thesis introduces methods to re-use the subspace or Eigen-space information of a matrix from a previous design or frequency to solve the next incremental problem faster.