Combined fast multipole-QR compression technique for solving electrically small to large structures for broadband applications
First Claim
1. A machine-implemented method for efficiently solving for a desired parameter of a system or device that includes either or both electrically large elements operating at relatively higher frequencies, and electrically small elements operating at relatively lower frequencies, comprising the steps of:
- (a) setting up the system or device as a predefined structure that enables a solution for the desired parameter to be determined, the predefined structure including a plurality of elements, wherein the plurality of elements include;
(i) electrically large elements, but not electrically small elements;
or(ii) electrically small elements, but not electrically large elements;
or(iii) both electrically large elements and electrically small elements;
(b) executing an iterative solver that determines 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 system or device;
(c) logically combining the matrix vector products for the electrically large elements and the electrically small elements, and determining a net delta for a combination of the matrix vector products;
(d) iteratively repeating steps (b) and (c) as necessary, until a subsequent net delta has been determined that is within a predefined limit;
(f) once a subsequent net delta has been determined that is within the predefined limit, employing said matrix vector products that were last determined to obtain a solution for the desired parameter; and
(g) presenting the solution for the desired parameter to a user in a tangible form.
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Accused Products
Abstract
An approach that efficiently solves for a desired parameter of a system or device that can include both electrically large fast multipole method (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.
11 Citations
21 Claims
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1. A machine-implemented method for efficiently solving for a desired parameter of a system or device that includes either or both electrically large elements operating at relatively higher frequencies, and electrically small elements operating at relatively lower frequencies, comprising the steps of:
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(a) setting up the system or device as a predefined structure that enables a solution for the desired parameter to be determined, the predefined structure including a plurality of elements, wherein the plurality of elements include; (i) electrically large elements, but not electrically small elements;
or(ii) electrically small elements, but not electrically large elements;
or(iii) both electrically large elements and electrically small elements; (b) executing an iterative solver that determines 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 system or device; (c) logically combining the matrix vector products for the electrically large elements and the electrically small elements, and determining a net delta for a combination of the matrix vector products; (d) iteratively repeating steps (b) and (c) as necessary, until a subsequent net delta has been determined that is within a predefined limit; (f) once a subsequent net delta has been determined that is within the predefined limit, employing said matrix vector products that were last determined to obtain a solution for the desired parameter; and (g) presenting the solution for the desired parameter to a user in a tangible form. - View Dependent Claims (2, 3, 4, 5, 6, 7, 8, 9, 10, 11)
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12. Apparatus for efficiently solving for a desired parameter of a system or device that includes either or both electrically large elements operating at relatively higher frequencies, and electrically small elements operating at relatively lower frequencies, comprising:
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(a) a memory for storing machine executable instructions; (b) a user interface that enables input and output; and (c) a processor that is coupled to the memory and to the user interface, the processor executing the machine executable instructions to carry out a plurality of functions, including; (i) setting up the system or device as a predefined structure that enables a solution for the desired parameter to be determined, the predefined structure including a plurality of elements, wherein the plurality of elements include; (1) electrically large elements, but not electrically small elements;
or(2) electrically small elements, but not electrically large elements;
or(3) both electrically large elements and electrically small elements; (ii) executing an iterative solver that determines 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 system or device; (iii) logically combining the matrix vector products for the electrically large elements and the electrically small elements, and determining a net delta for a combination of the matrix vector products; (iv) iteratively repeating steps (b) and (c) as necessary, until a subsequent net delta has been determined that is within a predefined limit; (v) once a subsequent net delta has been determined that is within the predefined limit, employing said matrix vector products that were last determined to obtain a solution for the desired parameter; and (vi) presenting the solution for the desired parameter to a user in a tangible form. - View Dependent Claims (13, 14, 15, 16, 17, 18, 19, 20, 21)
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Specification