公开(公告)号：US07359929B2

公开(公告)日：2008-04-15

申请号：US10706605

申请日：2003-11-12

申请人： Leung Tsang ,  Dong Chen ,  Qin Li

发明人： Leung Tsang ,  Dong Chen ,  Qin Li

IPC分类号： G06F7/38

CPC分类号： G06F17/5036 ,  G06F17/5018 ,  G06F2217/40

摘要： A technique for solving a set of wave equations in a region uses points arranged in a grid spanning the region or coefficients of wave expansion for objects located in the region. The grid points or the coefficients are partitioned into blocks on multiple levels, and block impedance matrices encoding the wave equations is derived for pairs of blocks. The block impedance matrix need not be calculated as it is written as the product of two non-square matrices, denoted U and V. Each of U and V have one linear dimension which is only of the order of the rank of the block impedance matrix levels. The rank is predetermined by coarse sampling. Two examples of the use of the invention are given: solving surface integral equations and Foldy Lax equations for partial waves.

摘要翻译： 用于求解一个区域中的一组波动方程的技术使用布置在横跨该区域的网格中的点或位于该区域中的对象的波形膨胀系数。 网格点或系数被分割成多个级别的块，并且为块对导出块编码波方程的块阻抗矩阵。 块阻抗矩阵不需要计算，因为它被写为两个非方阵矩阵的乘积，表示为U和V. U和V中的每一个具有一个线性尺寸，其仅为块阻抗矩阵的秩的级数 水平。 排名通过粗抽样预先确定。 给出了本发明使用的两个实例：求解表面积分方程和用于部分波的折叠Lax方程。

公开(公告)号：US20050102343A1

公开(公告)日：2005-05-12

申请号：US10706605

申请日：2003-11-12

申请人： Leung Tsang ,  Dong Chen ,  Qin Li

发明人： Leung Tsang ,  Dong Chen ,  Qin Li

IPC分类号： G06F7/38

CPC分类号： G06F17/5036 ,  G06F17/5018 ,  G06F2217/40

摘要： A technique for solving a set of wave equations in a region uses points arranged in a grid spanning the region or coefficients of wave expansion for objects located in the region. The grid points or the coefficients are partitioned into blocks on multiple levels, and block impedance matrices encoding the wave equations is derived for pairs of blocks. The block impedance matrix need not be calculated as it is written as the product of two non-square matrices, denoted U and V. Each of U and V have one linear dimension which is only of the order of the rank of the block impedance matrix levels. The rank is predetermined by coarse sampling. Two examples of the use of the invention are given: solving surface integral equations and Foldy Lax equations for partial waves.

摘要翻译： 用于求解一个区域中的一组波动方程的技术使用布置在横跨该区域的网格中的点或位于该区域中的对象的波形膨胀系数。 网格点或系数被分割成多个级别的块，并且为块对导出块编码波方程的块阻抗矩阵。 块阻抗矩阵不需要计算，因为它被写为两个非方阵矩阵的乘积，表示为U和V. U和V中的每一个具有一个线性尺寸，其仅为块阻抗矩阵的秩的级数 水平。 排名通过粗抽样预先确定。 给出了本发明使用的两个实例：求解表面积分方程和用于部分波的折叠Lax方程。

公开(公告)号：US07149666B2

公开(公告)日：2006-12-12

申请号：US10159965

申请日：2002-05-30

申请人： Leung Tsang ,  Houfei Chen ,  Chungchi Huang ,  Vikram Jandhyala

发明人： Leung Tsang ,  Houfei Chen ,  Chungchi Huang ,  Vikram Jandhyala

IPC分类号： G06F17/60

CPC分类号： G06F17/5036

摘要： Analyzing interactions between vias in multilayered electronic packages that include at least two spaced-apart conducting planes, and multiple vias that connect signal traces on different layers. Voltages at active via ports are represented as magnetic ring current sources, which generate electromagnetic modes inside the plane structure. Substantial electromagnetic coupling between vias occurs. A full-wave solution of multiple scattering among cylindrical vias in planar waveguides is derived using Foldy-Lax equations. By using the equivalence principle, the coupling is decomposed into interior and exterior problems. For the interior problem, the dyadic Green's function is expressed in terms of vector cylindrical waves and waveguide modes. The Foldy-Lax equations for multiple scattering among the cylindrical vias are applied, and waveguide modes are decoupled in the Foldy-Lax equations. The scattering matrix of coupling among vias is then calculated for use in determining signal reflection, transmission, and/or coupling in the electronics package.