The objective of this research is to solve the multiphysics design challenges in integrated power delivery for advanced electronic packaging and heterogeneous integration architectures. Embedded inductors, essential for efficient power delivery, must maintain high performance at elevated temperatures, minimizing Joule heating and inductance loss. Designing such components requires robust multiphysics modeling, yet conventional methods are computationally intensive. This thesis proposes solutions for both efficient embedded inductor design and computationally efficient multi-physics modeling. A dual-core inductor design is introduced, featuring two coils separated by magnetic cores and an air gap. This configuration enhances saturation current capacity and overall performance, mitigating the common low-saturation current limitation in embedded inductors. For multi-physics modeling, an augmented computational method is developed, using a frequency-domain approach with Fourier series–based Toeplitz matrices. This method provides a unified framework for transient electrical simulations and steady-state thermo-mechanical analysis, representing time-varying system elements in the frequency domain to improve stability and efficiency. To further accelerate computations, a parallelized version of the augmented method is implemented, leveraging modern CPU and GPU parallel architectures.