公开(公告)号：US08146043B2

公开(公告)日：2012-03-27

申请号：US12718309

申请日：2010-03-05

申请人： Lijun Jiang ,  Jason D. Morsey ,  Barry J. Rubin ,  Weng C. Chew ,  Mao-kun Li ,  Yuan Liu

发明人： Lijun Jiang ,  Jason D. Morsey ,  Barry J. Rubin ,  Weng C. Chew ,  Mao-kun Li ,  Yuan Liu

IPC分类号： G06F17/50

CPC分类号： G06F17/5036

摘要： A method for performing a signal integrity analysis on an integrated circuit (IC) that includes a plurality of scatterers by dividing the scatterers into subgroups using a nested Huygens' equivalence principle algorithm and solving a set of equations realized thereby with a reduced coupling matrix. The method includes decomposing the IC design into a plurality of small non-overlapping circuit sub-domains, wherein each of the sub-domains is formed as a small, enclosed region. Each sub-domain is analyzed independently of the other sub-domains using only electric fields to represent the interactions of each sub-domains with the other sub-domains as equivalent currents on equivalent surfaces of the plurality of sub-domains. Neighboring equivalent sub-domains are grouped together to form larger sub-domains using equivalent currents on equivalent surfaces to represent the interactions of the sub-domains. The steps of analyzing and grouping the sub-domains are repeated until the grouping approaches a box comprising the entire domain, and that the domain interactions between every sub-domain have been analyzed.

摘要翻译： 一种用于通过使用嵌套的惠更斯等效原理算法将散射体分成子组并且用减小的耦合矩阵求解由此实现的一组方程式来对包括多个散射体的集成电路（IC）进行信号完整性分析的方法。 该方法包括将IC设计分解为多个小的非重叠电路子域，其中每个子域形成为小的封闭区域。 仅使用电场来分析每个子域独立于其他子域，以将每个子域与其他子域的相互作用表示为多个子域的等效表面上的等效电流。 相邻的等效子域被分组在一起以形成较大的子域，使用等效表面上的等效电流来表示子域的相互作用。 重复分析和分组子域的步骤，直到分组接近包含整个域的框，并且分析了每个子域之间的域交互。

公开(公告)号：US20090144685A1

公开(公告)日：2009-06-04

申请号：US11754539

申请日：2007-05-29

申请人： Lijun Jiang ,  Jason D. Morsey

发明人： Lijun Jiang ,  Jason D. Morsey

IPC分类号： G06F17/50

CPC分类号： G06F17/5018 ,  G06F2217/16

摘要： The present invention a new closed-form double-layer integral for a rectangular basis. It is valid for both self integrals and non-self integrals. In general, the approach of the present invention contains only six (6) terms and is much simpler than indirect closed-form results, which has 24 terms.

摘要翻译： 本发明用于矩形的新的闭式双层积分。 它对于自我积分和非自我积分都是有效的。 通常，本发明的方法仅包含六（6）项，并且比具有24个术语的间接闭合形式结果简单得多。

公开(公告)号：US20090089021A1

公开(公告)日：2009-04-02

申请号：US11862434

申请日：2007-09-27

申请人： Lijun Jiang ,  Jason D. Morsey ,  Barry J. Rubin ,  Weng C. Chew ,  Mao-Kin Li ,  Yuan Liu

发明人： Lijun Jiang ,  Jason D. Morsey ,  Barry J. Rubin ,  Weng C. Chew ,  Mao-Kin Li ,  Yuan Liu

IPC分类号： G06F17/10 ,  G06G7/48

CPC分类号： G06F17/5036

摘要： A method for performing a signal integrity analysis on an integrated circuit (IC) that includes a plurality of scatterers by dividing the scatterers into subgroups using a nested Huygens' equivalence principle algorithm and solving a set of equations realized thereby with a reduced coupling matrix. The method includes decomposing the IC design into a plurality of small non-overlapping circuit sub-domains, wherein each of the sub-domains is formed as a small, enclosed region. Each sub-domain is analyzed independently of the other sub-domains using only electric fields to represent the interactions of each sub-domains with the other sub-domains as equivalent currents on equivalent surfaces of the plurality of sub-domains. Neighboring equivalent sub-domains are grouped together to form larger sub-domains using equivalent currents on equivalent surfaces to represent the interactions of the sub-domains. The steps of analyzing and grouping the sub-domains are repeated until the grouping approaches a box comprising the entire domain, and that the domain interactions between every sub-domain have been analyzed.

摘要翻译： 一种用于通过使用嵌套的惠更斯等效原理算法将散射体分成子组并且用减小的耦合矩阵求解由此实现的一组方程式来对包括多个散射体的集成电路（IC）进行信号完整性分析的方法。 该方法包括将IC设计分解为多个小的非重叠电路子域，其中每个子域形成为小的封闭区域。 仅使用电场来分析每个子域独立于其他子域，以将每个子域与其他子域的相互作用表示为多个子域的等效表面上的等效电流。 相邻的等效子域被分组在一起以形成较大的子域，使用等效表面上的等效电流来表示子域的相互作用。 重复分析和分组子域的步骤，直到分组接近包含整个域的框，并且分析了每个子域之间的域交互。

公开(公告)号：US07707527B2

公开(公告)日：2010-04-27

申请号：US11862434

申请日：2007-09-27

申请人： Lijun Jiang ,  Jason D. Morsey ,  Barry J. Rubin ,  Weng C. Chew ,  Mao-Kin Li ,  Yuan Liu

发明人： Lijun Jiang ,  Jason D. Morsey ,  Barry J. Rubin ,  Weng C. Chew ,  Mao-Kin Li ,  Yuan Liu

IPC分类号： G06F17/50

CPC分类号： G06F17/5036

摘要： A method for performing a signal integrity analysis on an integrated circuit (IC) that includes a plurality of scatterers by dividing the scatterers into subgroups using a nested Huygens' equivalence principle algorithm and solving a set of equations realized thereby with a reduced coupling matrix. The method includes decomposing the IC design into a plurality of small non-overlapping circuit sub-domains, wherein each of the sub-domains is formed as a small, enclosed region. Each sub-domain is analyzed independently of the other sub-domains using only electric fields to represent the interactions of each sub-domains with the other sub-domains as equivalent currents on equivalent surfaces of the plurality of sub-domains. Neighboring equivalent sub-domains are grouped together to form larger sub-domains using equivalent currents on equivalent surfaces to represent the interactions of the sub-domains. The steps of analyzing and grouping the sub-domains are repeated until the grouping approaches a box comprising the entire domain, and that the domain interactions between every sub-domain have been analyzed.

摘要翻译： 一种用于通过使用嵌套的惠更斯等效原理算法将散射体分成子组并且用减小的耦合矩阵求解由此实现的一组方程式来对包括多个散射体的集成电路（IC）进行信号完整性分析的方法。 该方法包括将IC设计分解为多个小的非重叠电路子域，其中每个子域形成为小的封闭区域。 仅使用电场来分析每个子域独立于其他子域，以将每个子域与其他子域的相互作用表示为多个子域的等效表面上的等效电流。 相邻的等效子域被分组在一起以形成较大的子域，使用等效表面上的等效电流来表示子域的相互作用。 重复分析和分组子域的步骤，直到分组接近包含整个域的框，并且分析了每个子域之间的域交互。

公开(公告)号：US20100161293A1

公开(公告)日：2010-06-24

申请号：US12718309

申请日：2010-03-05

申请人： Lijun Jiang ,  Jason D. Morsey ,  Barry J. Rubin ,  Weng C. Chew ,  Mao-kun Li ,  Yuan Liu

发明人： Lijun Jiang ,  Jason D. Morsey ,  Barry J. Rubin ,  Weng C. Chew ,  Mao-kun Li ,  Yuan Liu

IPC分类号： G06F17/11

CPC分类号： G06F17/5036

摘要： A method for performing a signal integrity analysis on an integrated circuit (IC) that includes a plurality of scatterers by dividing the scatterers into subgroups using a nested Huygens' equivalence principle algorithm and solving a set of equations realized thereby with a reduced coupling matrix. The method includes decomposing the IC design into a plurality of small non-overlapping circuit sub-domains, wherein each of the sub-domains is formed as a small, enclosed region. Each sub-domain is analyzed independently of the other sub-domains using only electric fields to represent the interactions of each sub-domains with the other sub-domains as equivalent currents on equivalent surfaces of the plurality of sub-domains. Neighboring equivalent sub-domains are grouped together to form larger sub-domains using equivalent currents on equivalent surfaces to represent the interactions of the sub-domains. The steps of analyzing and grouping the sub-domains are repeated until the grouping approaches a box comprising the entire domain, and that the domain interactions between every sub-domain have been analyzed.

摘要翻译： 一种用于通过使用嵌套的惠更斯等效原理算法将散射体分成子组并且用减小的耦合矩阵求解由此实现的一组方程式来对包括多个散射体的集成电路（IC）进行信号完整性分析的方法。 该方法包括将IC设计分解为多个小的非重叠电路子域，其中每个子域形成为小的封闭区域。 仅使用电场来分析每个子域独立于其他子域，以将每个子域与其他子域的相互作用表示为多个子域的等效表面上的等效电流。 相邻的等效子域被分组在一起以形成较大的子域，使用等效表面上的等效电流来表示子域的相互作用。 重复分析和分组子域的步骤，直到分组接近包含整个域的框，并且分析了每个子域之间的域交互。

公开(公告)号：US20080306716A1

公开(公告)日：2008-12-11

申请号：US12192481

申请日：2008-08-15

申请人： Peter Feldmann ,  Jason D. Morsey ,  Barry J. Rubin

发明人： Peter Feldmann ,  Jason D. Morsey ,  Barry J. Rubin

IPC分类号： G06F7/60 ,  G06F1/00 ,  G06G7/48

CPC分类号： G06F17/12

摘要： This invention relates to computing numerical solutions of linear systems of equations, specifically to implementing preconditioning of the coefficient matrix of such a system. The preconditioning applies to any coefficient matrix, dense or sparse, based on the solutions of a physical problem of unknown functions, commonly referred to as basis or interpolation functions, where the basis function spans more then one mesh element. Examples of such linear systems can result from, as examples, an electromagnetic analysis of printed circuit boards or field scattering in radar applications, fluid mechanics and acoustics. A method and system to compute a preconditioner for a coefficient matrix A that is compatible with the linear system of equations that provides basis function support over at least two mesh elements. Coupling of the preconditioner between partitions of a portioned mesh representation is only through basis functions at the partition boundaries.

摘要翻译： 本发明涉及计算线性方程组的数值解，具体涉及实现这种系统的系数矩阵的预处理。 基于未知函数的物理问题的解决方案，通常称为基础函数或插值函数，其中基函数跨越多于一个网格元素，该预处理适用于任何密集或稀疏的系数矩阵。 作为示例，这种线性系统的示例可以从印刷电路板的电磁分析或雷达应用中的场散射，流体力学和声学等方面得到。 一种用于计算系数矩阵A的预处理器的方法和系统，该系数矩阵A与在至少两个网格元素上提供基函数支持的线性方程组兼容。 分段网格表示的分区之间的预处理器的耦合仅通过分区边界处的基函数。

公开(公告)号：US07933751B2

公开(公告)日：2011-04-26

申请号：US12192459

申请日：2008-08-15

申请人： Peter Feldmann ,  Jason D. Morsey ,  Barry J. Rubin

发明人： Peter Feldmann ,  Jason D. Morsey ,  Barry J. Rubin

IPC分类号： G06F17/50 ,  G06G7/48 ,  G06G7/50 ,  G06G7/62 ,  G01N15/08 ,  G01F7/00 ,  G01F17/00

CPC分类号： G06F17/12

摘要： This invention relates to computing numerical solutions of linear systems of equations, specifically to implementing preconditioning of the coefficient matrix of such a system. The preconditioning applies to any coefficient matrix, dense or sparse, based on the solutions of a physical problem of unknown functions, commonly referred to as basis or interpolation functions, where the basis function spans more then one mesh element. Examples of such linear systems can result from, as examples, an electromagnetic analysis of printed circuit boards or field scattering in radar applications, fluid mechanics and acoustics. A method and system to compute a preconditioner for a coefficient matrix A that is compatible with the linear system of equations that provides basis function support over at least two mesh elements. Coupling of the preconditioner between partitions of a portioned mesh representation is only through basis functions at the partition boundaries.

摘要翻译： 本发明涉及计算线性方程组的数值解，具体涉及实现这种系统的系数矩阵的预处理。 基于未知函数的物理问题的解决方案，通常称为基础函数或插值函数，其中基函数跨越多于一个网格元素，该预处理适用于任何密集或稀疏的系数矩阵。 作为示例，这种线性系统的示例可以从印刷电路板的电磁分析或雷达应用中的场散射，流体力学和声学等方面得到。 一种用于计算系数矩阵A的预处理器的方法和系统，该系数矩阵A与在至少两个网格元素上提供基函数支持的线性方程组兼容。 分段网格表示的分区之间的预处理器的耦合仅通过分区边界处的基函数。

公开(公告)号：US07933752B2

公开(公告)日：2011-04-26

申请号：US12192481

申请日：2008-08-15

申请人： Peter Feldmann ,  Jason D. Morsey ,  Barry J. Rubin

发明人： Peter Feldmann ,  Jason D. Morsey ,  Barry J. Rubin

IPC分类号： G06F7/60 ,  G06G7/48 ,  G06G7/50 ,  G01V1/40 ,  G01F1/00 ,  G01F17/00 ,  G01R15/00

CPC分类号： G06F17/12

摘要： This invention relates to computing numerical solutions of linear systems of equations, specifically to implementing preconditioning of the coefficient matrix of such a system. The preconditioning applies to any coefficient matrix, dense or sparse, based on the solutions of a physical problem of unknown functions, commonly referred to as basis or interpolation functions, where the basis function spans more then one mesh element. Examples of such linear systems can result from, as examples, an electromagnetic analysis of printed circuit boards or field scattering in radar applications, fluid mechanics and acoustics. A method and system to compute a preconditioner for a coefficient matrix A that is compatible with the linear system of equations that provides basis function support over at least two mesh elements. Coupling of the preconditioner between partitions of a portioned mesh representation is only through basis functions at the partition boundaries.

摘要翻译： 本发明涉及计算线性方程组的数值解，具体涉及实现这种系统的系数矩阵的预处理。 基于未知函数的物理问题的解决方案，通常称为基础函数或插值函数，其中基函数跨越多于一个网格元素，该预处理适用于任何密集或稀疏的系数矩阵。 作为示例，这种线性系统的示例可以从印刷电路板的电磁分析或雷达应用中的场散射，流体力学和声学等方面得到。 一种用于计算系数矩阵A的预处理器的方法和系统，该系数矩阵A与在至少两个网格元素上提供基函数支持的线性方程组兼容。 分段网格表示的分区之间的预处理器的耦合仅通过分区边界处的基函数。

公开(公告)号：US20090037157A1

公开(公告)日：2009-02-05

申请号：US12192459

申请日：2008-08-15

申请人： Peter Feldmann ,  Jason D. Morsey ,  Barry J. Rubin

发明人： Peter Feldmann ,  Jason D. Morsey ,  Barry J. Rubin

IPC分类号： G06F7/60 ,  G06G7/48

CPC分类号： G06F17/12

摘要： This invention relates to computing numerical solutions of linear systems of equations, specifically to implementing preconditioning of the coefficient matrix of such a system. The preconditioning applies to any coefficient matrix, dense or sparse, based on the solutions of a physical problem of unknown functions, commonly referred to as basis or interpolation functions, where the basis function spans more then one mesh element. Examples of such linear systems can result from, as examples, an electromagnetic analysis of printed circuit boards or field scattering in radar applications, fluid mechanics and acoustics. A method and system to compute a preconditioner for a coefficient matrix A that is compatible with the linear system of equations that provides basis function support over at least two mesh elements. Coupling of the preconditioner between partitions of a portioned mesh representation is only through basis functions at the partition boundaries.

摘要翻译： 本发明涉及计算线性方程组的数值解，具体涉及实现这种系统的系数矩阵的预处理。 基于未知函数的物理问题的解决方案，通常称为基础函数或插值函数，其中基函数跨越多于一个网格元素，该预处理适用于任何密集或稀疏的系数矩阵。 作为示例，这种线性系统的示例可以从印刷电路板的电磁分析或雷达应用中的场散射，流体力学和声学等方面得到。 一种用于计算系数矩阵A的预处理器的方法和系统，该系数矩阵A与在至少两个网格元素上提供基函数支持的线性方程组兼容。 分段网格表示的分区之间的预处理器的耦合仅通过分区边界处的基函数。

公开(公告)号：US07418370B2

公开(公告)日：2008-08-26

申请号：US10815432

申请日：2004-03-31

申请人： Peter Feldmann ,  Jason D. Morsey ,  Barry J. Rubin

发明人： Peter Feldmann ,  Jason D. Morsey ,  Barry J. Rubin

IPC分类号： G06F7/60 ,  G06G7/48 ,  G02N15/08 ,  G01F1/00 ,  G01R15/00

CPC分类号： G06F17/12

摘要： This invention relates to computing numerical solutions of linear systems of equations, specifically to implementing preconditioning of the coefficient matrix of such a system. The preconditioning applies to any coefficient matrix, dense or sparse, based on the solutions of a physical problem of unknown functions, commonly referred to as basis or interpolation functions, where the basis function spans more then one mesh element. Examples of such linear systems can result from, as examples, an electromagnetic analysis of printed circuit boards or field scattering in radar applications, fluid mechanics and acoustics. A method and system to compute a preconditioner for a coefficient matrix A that is compatible with the linear system of equations that provides basis function support over at least two mesh elements. Coupling of the preconditioner between partitions of a portioned mesh representation is only through basis functions at the partition boundaries.

摘要翻译： 本发明涉及计算线性方程组的数值解，具体涉及实现这种系统的系数矩阵的预处理。 基于未知函数的物理问题的解决方案，通常称为基础函数或插值函数，其中基函数跨越多于一个网格元素，该预处理适用于任何密集或稀疏的系数矩阵。 作为示例，这种线性系统的示例可以从印刷电路板的电磁分析或雷达应用中的场散射，流体力学和声学等方面得到。 一种用于计算系数矩阵A的预处理器的方法和系统，该系数矩阵A与在至少两个网格元素上提供基函数支持的线性方程组兼容。 分段网格表示的分区之间的预处理器的耦合仅通过分区边界处的基函数。