INTRODUCTION The recent trend toward more extreme periods of drought has been a shock to the residents of the Pacific Northwest-many of whom have relied upon heavy water-use in the summer months in order to make a liv...INTRODUCTION The recent trend toward more extreme periods of drought has been a shock to the residents of the Pacific Northwest-many of whom have relied upon heavy water-use in the summer months in order to make a living(i.e.producers of grass seed and sod,berries,or nursery crops),or to maintain their landscapes at high levels(i.e.certain homeowners,recreational facilities,or commercial properties).Further-more,population growth has reached the point where even an average year of pre-cipitation has proven insufficient for urbanities that had not previously experienced issues with water scarcity(McDonald et al.,2011).This modern climate scenario has forced people of the Pacific Northwest,and people from all around the world,to rethink their water-use strategies,as the global trend has shifted toward greater sustainability(Tilman,2001;McDonald et al.,2011).展开更多
In solving application problems, many largesscale nonlinear systems of equations result in sparse Jacobian matrices. Such nonlinear systems are called sparse nonlinear systems. The irregularity of the locations of non...In solving application problems, many largesscale nonlinear systems of equations result in sparse Jacobian matrices. Such nonlinear systems are called sparse nonlinear systems. The irregularity of the locations of nonzero elements of a general sparse matrix makes it very difficult to generally map sparse matrix computations to multiprocessors for parallel processing in a well balanced manner. To overcome this difficulty, we define a new storage scheme for general sparse matrices in this paper. With the new storage scheme, we develop parallel algorithms to solve large-scale general sparse systems of equations by interval Newton/Generalized bisection methods which reliably find all numerical solutions within a given domain.In Section 1, we provide an introduction to the addressed problem and the interval Newton's methods. In Section 2, some currently used storage schemes for sparse sys-terns are reviewed. In Section 3, new index schemes to store general sparse matrices are reported. In Section 4, we present a parallel algorithm to evaluate a general sparse Jarobian matrix. In Section 5, we present a parallel algorithm to solve the correspond-ing interval linear 8ystem by the all-row preconditioned scheme. Conclusions and future work are discussed in Section 6.展开更多
文摘INTRODUCTION The recent trend toward more extreme periods of drought has been a shock to the residents of the Pacific Northwest-many of whom have relied upon heavy water-use in the summer months in order to make a living(i.e.producers of grass seed and sod,berries,or nursery crops),or to maintain their landscapes at high levels(i.e.certain homeowners,recreational facilities,or commercial properties).Further-more,population growth has reached the point where even an average year of pre-cipitation has proven insufficient for urbanities that had not previously experienced issues with water scarcity(McDonald et al.,2011).This modern climate scenario has forced people of the Pacific Northwest,and people from all around the world,to rethink their water-use strategies,as the global trend has shifted toward greater sustainability(Tilman,2001;McDonald et al.,2011).
文摘In solving application problems, many largesscale nonlinear systems of equations result in sparse Jacobian matrices. Such nonlinear systems are called sparse nonlinear systems. The irregularity of the locations of nonzero elements of a general sparse matrix makes it very difficult to generally map sparse matrix computations to multiprocessors for parallel processing in a well balanced manner. To overcome this difficulty, we define a new storage scheme for general sparse matrices in this paper. With the new storage scheme, we develop parallel algorithms to solve large-scale general sparse systems of equations by interval Newton/Generalized bisection methods which reliably find all numerical solutions within a given domain.In Section 1, we provide an introduction to the addressed problem and the interval Newton's methods. In Section 2, some currently used storage schemes for sparse sys-terns are reviewed. In Section 3, new index schemes to store general sparse matrices are reported. In Section 4, we present a parallel algorithm to evaluate a general sparse Jarobian matrix. In Section 5, we present a parallel algorithm to solve the correspond-ing interval linear 8ystem by the all-row preconditioned scheme. Conclusions and future work are discussed in Section 6.
