This thesis describes a new approach to accelerate the simulation of the steady-state response of nonlinear circuits using the Harmonic Balance (HB) technique. The approach presented in this work focuses on direct factorization of the sparse Jacobian matrix of the HB nonlinear equations using a Graphics Processing Unit (GPU) platform. This approach exploits the heterogeneous structure of the Jacobian matrix. The computational core of the proposed approach is based on developing a block-wise version of the KLU factorization algorithm, where scalar arithmetic operations are replaced by block-aware matrix operations. For a large number of harmonics, or excitation tones, or both the Block-KLU (BKLU) approach effectively raises the ratio of floating-point operations to other operations and, therefore, becomes an ideal vehicle for implementation on a GPU-based platform. Motivated by this fact, a GPU-based Hybrid Block KLU framework is developed to implement the BKLU. The proposed approach in this thesis is named Hybrid-BKLU. The Hybrid-BKLU is implemented in two parts, on the host CPU and on the graphic card’s GPU, using the OpenCL heterogeneous parallel programming language. To show the efficiency of the Hybrid-BKLU approach, its performance is compared with BKLU approach performing HB analysis on several test circuits. The Hybrid-BKLU approach yields speedup by up to 89 times over conventional BKLU on CPU.

This thesis describes a new approach to accelerate the simulation of the steady-state response of nonlinear circuits using the Harmonic Balance (HB) technique. The approach presented in this work focuses on direct factorization of the sparse Jacobian matrix of the HB nonlinear equations using a Graphics Processing Unit (GPU) platform. This approach exploits the heterogeneous structure of the Jacobian matrix. The computational core of the proposed approach is based on developing a block-wise version of the KLU factorization algorithm, where scalar arithmetic operations are replaced by block-aware matrix operations. For a large number of harmonics, or excitation tones, or both the Block-KLU (BKLU) approach effectively raises the ratio of floating-point operations to other operations and, therefore, becomes an ideal vehicle for implementation on a GPU-based platform. Motivated by this fact, a GPU-based Hybrid Block KLU framework is developed to implement the BKLU. The proposed approach in this thesis is named Hybrid-BKLU. The Hybrid-BKLU is implemented in two parts, on the host CPU and on the graphic card’s GPU, using the OpenCL heterogeneous parallel programming language. To show the efficiency of the Hybrid-BKLU approach, its performance is compared with BKLU approach performing HB analysis on several test circuits. The Hybrid-BKLU approach yields speedup by up to 89 times over conventional BKLU on CPU.