Acceleration of the partial element equivalent circuit method with uniform tessellation—part I: Identification of geometrical signatures

Abstract

Electromagnetic numerical modeling has become crucial for the design deployment and operation of new electrical and electronic devices and systems especially for its capability to address electromagnetic compatibility and interference issues. In this regard, accurate and efficient numerical techniques are required for effective and fast virtual prototyping. This paper presents a novel technique to speedup the computation of partial elements describing the magnetic and electric field couplings in the framework of the partial element equivalent circuit method. When dealing with uniform tessellation of 3D geometries, including Manhattan-type meshes and also nonorthogonal ones characterized by hexahedra with comparable sizes, a huge number of configurations are repeated under only translation and rotation transformations. Through an efficient identification of these geometrical signatures, the calculation of volume and surface integrals required to fill the partial element matrices, namely, partial inductances and coefficients of potential, can be significantly accelerated. To this aim, assuming a uniform tessellation of volumes and surfaces, a complete algorithm is presented to systematically identify all the signatures and manage them, thus allowing a significant speedup of the partial element matrices filling-in process.Being based on a systematic identification of the different patterns, the proposed method does not introduce any approximation. Numerical examples are presented pointing out the correctness and efficiency of the proposed approach. KEYWORDS binary search, frequency-domain analysis, integral equations, memory management, partial element equivalent circuit (PEEC) method, partial elements computation, speedup techniques The analysis of electromagnetic compatibility, signal integrity, and power integrity issues in high-speed systems requires accurate models of interconnects and packaging that can be included in a SPICE-level simulation. Hence, much effort has been devoted in the last 20 years to develop computational models of 3D structures drawn directly from the interconnect or package geometry, and numerical methods have gained popularity for their capability to perform virtual prototyping. Furthermore, the fast and continuous penetration of electronic sensing, communication, and actuation technologies-examples include smart cities and grids, intelligent medical devices and systems, more electrical vehicles Int J Numer Model. 2018;31:e2307.wileyonlinelibrary.com/journal/jnm

Acceleration of the partial element equivalent circuit method with uniform tessellation—Part II: Frequency domain solver with interpolation and reuse of partial elements

“…In Part I, the PEEC‐IGS algorithm has been introduced to limit the computations of these integrals to a reduced subset of partial elements without introducing any approximation. The basic idea of the proposed approach relies on the fact that when an integral between 2 inductive or capacitive cells is computed for the first time, the result is stored and can be reused any time the same geometrical structure of the problem occurs.…”

“…The basic idea of the proposed approach relies on the fact that when an integral between 2 inductive or capacitive cells is computed for the first time, the result is stored and can be reused any time the same geometrical structure of the problem occurs. Before describing the algorithm, it is useful to introduce the data structures used in Romano, Lombardi and Antonini: matrix : it stores as row vectors the 9 geometrical features used to identify a configuration (see Romano, Lombardi and Antonini, being T the number of the stored geometrical configurations); vector : it stores in each position i the sum of the i th row in T . Such vector has been introduced in Romano, Lombardi and Antonini to perform the searching of the different geometrical configurations. vector : it stores in each position i the values of the volume or surface integral of the geometrical configurations written into T ( i ,:). …”

“…At this point, the IGS algorithm can be summarized as reported in procedure IGS‐ALGORITHM given in Figure (for the detailed description, see Romano, Lombardi and Antonini).…”

“…In Part I of this work, the PEEC‐IGS (identification of geometrical signatures) algorithm has been introduced to compute a minimal set of partial elements that allows to fill the entire partial inductances and coefficients of potential matrices avoiding the computation of several numerical integrals for volumes and surfaces that requires O ( W 6 ) and O ( W 4 ) operations, respectively, being W the order of integration. Furthermore, to accelerate the fill‐in of the impedance matrix, several techniques have been proposed in the last years.…”

On the passivity of the quasi‐static partial element equivalent circuit method

“…PEEC uses a circuit interpretation of the electric field integral equation (EFIE), thus allowing to handle complex problems involving EM fields and circuits . It has recently extended to electrothermal problems and accelerated by an innovative approach exploiting the redundancy in the magnetic and electric fields interactions . The PEEC equivalent circuits are usually connected with terminations such as drivers and receivers in a time domain circuit simulator (eg, SPICE‐like circuit solvers).…”