公开(公告)号：US08250069B2

公开(公告)日：2012-08-21

申请号：US12250990

申请日：2008-10-14

申请人： Vikram Jandhyala

发明人： Vikram Jandhyala

IPC分类号： G06F7/00 ,  G06F17/30

CPC分类号： G06F17/30864

摘要： A novel approach to determining PageRank for web pages views the problem as being comparable to solving for an electromagnetic field problem. This view of ranking web pages enables appropriate entries for a matrix G of the web (or a subset), so that fast-solver techniques can be employed to iterate G, solving for ranks, or a dominant eigenstructure, achieving an O(N log N) performance in time and memory requirements. The specific solver technique that is used can be, for example, a fast multi-pole method (FMM), or a multilevel low-rank compression method. Once the problem is correctly formulated, it is not necessary to create the matrix G. Local information can be queried on demand by the solver. This approach can also be used to determine different scores of web pages, such as TrustRank, which is indicative of their trustworthiness.

摘要翻译： 确定网页的PageRank的新颖方法将问题视为与电磁场问题的解决相当的问题。 排名网页的这种观点使得web（或子集）的矩阵G能够进行适当的输入，从而可以采用快速求解技术来迭代G，解决等级或主要特征结构，从而实现O（N log N）时间和记忆要求的表现。 所使用的具体求解器技术可以是例如快速多极方法（FMM）或多级低等级压缩方法。 一旦问题得到正确的制定，就没有必要创建矩阵G.地方信息可以由求解者根据需要进行查询。 这种方法也可用于确定不同分数的网页，如TrustRank，这表明其可信赖性。

公开(公告)号：US20100057408A1

公开(公告)日：2010-03-04

申请号：US12199277

申请日：2008-08-27

申请人： Vikram Jandhyala ,  Indranil Chowdhury

发明人： Vikram Jandhyala ,  Indranil Chowdhury

IPC分类号： G06F7/60 ,  G06F17/10

CPC分类号： G06F17/5009 ,  G06F2217/16

摘要： In one exemplary approach, a Schur complement-based boundary element method (BEM) is employed for predicting the motion of arbitrarily shaped three-dimensional particles under combined external and fluidic force fields. The BEM relies on modeling the surface of the computational domain, significantly reducing the number of unknowns when compared to volume-based methods. In addition, the Schur complement-based scheme enables a static portion of the computation to be computed only once for use in subsequent time steps, which leads to a tremendous reduction in solution time during time-stepping in the microfluidic domain. Parallelized oct-tree based O(N) multilevel iterative solvers are also used to accelerate the setup and solution costs.

摘要翻译： 在一个示例性方法中，采用基于Schur补码的边界元方法（BEM）来预测组合的外部和流体力场下的任意形状的三维粒子的运动。 BEM依赖于​​对计算领域的表面建模，与基于体积的方法相比，显着减少了未知数。 此外，基于Schur补码的方案使得计算的静态部分仅计算一次，以用于随后的时间步长，这导致在微流体域中的时间步长期间解决时间的巨大降低。 基于并行八进制的O（N）多级迭代求解器也用于加速设置和解决方案成本。

公开(公告)号：US20080027689A1

公开(公告)日：2008-01-31

申请号：US11778369

申请日：2007-07-16

申请人： Vikram Jandhyala ,  Indranil Chowdhury

发明人： Vikram Jandhyala ,  Indranil Chowdhury

IPC分类号： G06F17/10 ,  G06F7/60

CPC分类号： G06F17/5009 ,  G06F2217/16

摘要： An approach that efficiently solves for a desired parameter of a system or device that can include both electrically large FMM elements, and electrically small QR elements. The system or device is setup as an oct-tree structure that can include regions of both the FMM type and the QR type. An iterative solver is then used to determine a first matrix vector product for any electrically large elements, and a second matrix vector product for any electrically small elements that are included in the structure. These matrix vector products for the electrically large elements and the electrically small elements are combined, and a net delta for a combination of the matrix vector products is determined. The iteration continues until a net delta is obtained that is within predefined limits. The matrix vector products that were last obtained are used to solve for the desired parameter.

摘要翻译： 有效地解决可以包括电大FMM元件和电小QR元件的系统或装置的期望参数的方法。 系统或设备被设置为可以包括FMM类型和QR类型的区域的八叉树结构。 然后使用迭代求解器来确定用于任何电大元件的第一矩阵矢量积，以及用于包括在该结构中的任何电小元件的第二矩阵矢量积。 用于电大元件和电小元件的这些矩阵向量积被组合，并且确定矩阵向量积的组合的净增量。 迭代继续，直到得到在预定义限度内的净增量。 最后获得的矩阵矢量产品用于求解所需参数。

公开(公告)号：US08725484B2

公开(公告)日：2014-05-13

申请号：US13082818

申请日：2011-04-08

申请人： Vikram Jandhyala ,  Swagato Chakraborty ,  Dipanjan Gope

发明人： Vikram Jandhyala ,  Swagato Chakraborty ,  Dipanjan Gope

IPC分类号： G06F17/50

CPC分类号： G06F17/5018 ,  G06F17/5036 ,  G06F2217/16

摘要： Redundancy extraction in electromagnetic simulation of an electronic device/system includes discretizing first and second spaced conductive layers of a computer model of an electronic device/system into first and second meshes M1 and M2. For each edge between cells of each mesh, a current flow across the edge in response to application of an exemplary bias to the geometry is determined. A square impedance matrix Z* is determined which, for each instance of equal magnitude and opposite direction current flows (EMODCF) in edges E1 and E2 of M1 and M2, has one less row and one less column than the total number of edges in M1 and M2. A voltage column vector V* is also determined which, for each instance of EMODCF, has one less row than the total number of edges in M1 and M2. A current column vector [I*]=[V*]/[Z*] is then determined.

摘要翻译： 电子设备/系统的电磁仿真中的冗余提取包括将电子设备/系统的计算机模型的第一和第二间隔导电层离散成第一和第二网格M1和M2。 对于每个网格的单元之间的每个边缘，确定响应于对几何形状的示例性偏置的应用而跨越边缘的电流。 确定矩形阻抗矩阵Z *，对于M1和M2的边缘E1和E2中的相等幅度和相反方向电流（EMODCF）的每个情况，对于M1中的边缘的总数少一列，少于M1中的边的总数 和M2。 还确定电压列向量V *，对于EMODCF的每个实例，对于M1和M2中的边缘总数少一行。 然后确定当前列向量[I *] = [V *] / [Z *]。

公开(公告)号：US20120046922A1

公开(公告)日：2012-02-23

申请号：US12859531

申请日：2010-08-19

申请人： Vikram Jandhyala

发明人： Vikram Jandhyala

IPC分类号： G06F17/50

CPC分类号： G06F17/5018 ,  G06F17/5095 ,  G06F2217/04

摘要： In a method of electronic design automation, discretized meshes of layers of current conducting materials of a computerized device model are determined. Each discretized mesh corresponds to the current conducting material of one model layer. For each discretized mesh, a corresponding impedance matrix having cells is determined. Each cell includes an impedance value Zij which is based on a voltage (Vi) induced in a cell i of the discretized mesh due to a current (Ij) flowing in a cell j of the discretized mesh. A subset of the cells, including impedance values, of the impedance matrices is dispatched to node computers via an electronic communications network. In response to dispatching the cells of the impedance matrices, charge densities estimated by the node computers to exist on a subset of the cells of the discretized meshes are returned.

摘要翻译： 在电子设计自动化的方法中，确定计算机化设备模型的电流导电材料层的离散网格。 每个离散网格对应于一个模型层的当前导电材料。 对于每个离散网格，确定具有单元的对应阻抗矩阵。 每个单元包括阻抗值Zij，其基于由离散化网格的单元格j中流动的电流（Ij）而导致的离散网格的单元i中感应的电压（Vi）。 通过电子通信网络将阻抗矩阵的单元的子集（包括阻抗值）调度到节点计算机。 响应于调度阻抗矩阵的单元，返回由节点计算机估计存在于离散化网格的单元的子集上的电荷密度。

公开(公告)号：US20100094904A1

公开(公告)日：2010-04-15

申请号：US12250990

申请日：2008-10-14

申请人： Vikram Jandhyala

发明人： Vikram Jandhyala

IPC分类号： G06F7/06 ,  G06F17/30

CPC分类号： G06F17/30864

摘要： A novel approach to determining PageRank for web pages views the problem as being comparable to solving for an electromagnetic field problem. This view of ranking web pages enables appropriate entries for a matrix G of the web (or a subset), so that fast-solver techniques can be employed to iterate G, solving for ranks, or a dominant eigenstructure, achieving an O(N log N) performance in time and memory requirements. The specific solver technique that is used can be, for example, a fast multi-pole method (FMM), or a multilevel low-rank compression method. Once the problem is correctly formulated, it is not necessary to create the matrix G. Local information can be queried on demand by the solver. This approach can also be used to determine different scores of web pages, such as TrustRank, which is indicative of their trustworthiness.

摘要翻译： 确定网页的PageRank的新颖方法将问题视为与电磁场问题的解决相当的问题。 排名网页的这种观点使得web（或子集）的矩阵G能够进行适当的输入，从而可以采用快速求解技术来迭代G，解决等级或主要特征结构，从而实现O（N log N）时间和记忆要求的表现。 所使用的具体求解器技术可以是例如快速多极方法（FMM）或多级低等级压缩方法。 一旦问题得到正确的制定，就没有必要创建矩阵G.地方信息可以由求解者根据需要进行查询。 这种方法也可用于确定不同分数的网页，如TrustRank，这表明其可信赖性。