The 2005 International Conference on Preconditioning Techniques for Large Sparse Matrix Problems in Industrial Applications; May 19-21, 2005; Atlanta, GA

许多大规模科学应用和工业数值模拟的计算核心通常是一个大型稀疏矩阵问题，它通常消耗了模拟所需的总计算时间的很大一部分。许多矩阵问题是线性方程组的形式，尽管其他类型的问题，如特征值计算，也可能发生。传统的求解大型稀疏矩阵方程组的方法是直接法。这种方法在工业上通常是首选的，因为直接求解器对于中等规模的问题是鲁棒和有效的。然而，技术进步的空前速度导致了需要处理的矩阵规模的急剧增长。例如，三维模拟的存储要求使得直接方法过于昂贵。迭代法是唯一可行的方法，但迭代法缺乏直接法的鲁棒性。当矩阵条件很差时，它们经常失效。这就是当前对大型稀疏矩阵问题的预处理技术的巨大兴趣的原因：预处理器显着提高了迭代算法的鲁棒性和性能。尽管在过去的几年里，预处理技术取得了很大的进展，迭代求解器仍然不总是完全可靠和有效的。拟议的会议，在一年两次的预处理会议系列的第四，旨在解决与一般稀疏矩阵问题的解决方案在大规模的真实的应用和工业环境中的复杂问题。应用科学家和工业用户感兴趣的与稀疏矩阵软件相关的问题通常与学术界关注的问题相当不同。例如，对于应用科学家或工业用户来说，提高鲁棒性可能比找到一种提高速度的方法重要得多。内存使用也是一个重要的考虑因素，但在稀疏矩阵求解器的学术研究中很少考虑。作为最后一个例子，在应用中求解的线性系统几乎总是一些非线性迭代的一部分（例如，考虑线性和非线性部分之间的耦合是很重要的，而不是只关注线性系统。本次会议的发言者将讨论稀疏矩阵问题的预处理技术领域的一些最新发展。会议将允许来自学术界、工业界和政府实验室的参与者交流这一领域的研究成果，并根据新兴的范例（如并行处理和面向对象编程）探索可能的新方向。

The innermost computational kernel of many large-scale scientific applications andindustrial numerical simulations is often a large sparse matrix problem, which typicallyconsumes a significant portion of the overall computational time required by the simulation.Many of the matrix problems are in the form of systems of linear equations, although othertypes of problems, such as eigenvalue calculations, can occur too. A tremendous impactwill be made if the performance of these sparse matrix solvers can be improved.A traditional approach to solving large sparse matrix equations is to use directmethods. This approach is often preferred in industry because direct solvers arerobust and effective for moderate size problems. However, the unprecedented paceof the advance in technology has led to a dramatic growth in the size of the matricesto be handled. For example, the storage requirement for three-dimensional simulations makesdirect methods prohibitively expensive. Iterative techniques are the only viable alternative.Unfortunately, iterative methods lack the robustness of direct methods. They often failwhen the matrix is very ill-conditioned. This is the reason for the tremendous currentinterest in preconditioning techniques for large sparse matrix problems: preconditionersdramatically improve the robusteness and performance of iterative algorithms. In spite of much progress on preconditioning techniques over the last few years,iterative solvers are still not always completely reliable and efficient. The proposedconference, the fourth in a series of biannual meetings on preconditioning, intends toaddress the complex issues related to the solution of general sparse matrix problemsin large-scale real applications and in industrial settings. The issues related to sparse matrix software that are of interest to application scientists and industrialusers are often fairly different from those on which the academic community is focused.For example, for an application scientist or an industrial user, improving robustnessmay be far more important than finding a method that would gain speed. Memory usage isalso an important consideration, but is seldom accounted for in academic research onsparse matrix solvers. As a last example, linear systems solved in applications arealmost always part of some nonlinear iteration (e.g., Newton) or optimization loop.It is important to consider the coupling between the linear and nonlinear parts, insteadof focusing on the linear systems alone. The speakers of this conference will discusssome of the latest developments in the field of preconditioning techniques for sparsematrix problems. The conference will allow participants from academia, industry andgovernment labs to exchange findings in this area and to explore possible new directionsin light of emerging paradigms, such as parallel processing and object-oriented programming.