In this paper, we investigate resource allocation algorithm design for large intelligent reflecting surface (IRS)-assisted simultaneous wireless information and power transfer (SWIPT) systems. To this end, we adopt a physics-based IRS model that, unlike the conventional IRS model, takes into account the impact of the incident and reflection angles of the impinging electromagnetic wave on the reflected signal. To facilitate efficient resource allocation design for large IRSs, we employ a scalable optimization framework, where the IRS is partitioned into several tiles and the phase shift elements of each tile are jointly designed to realize different transmission modes. Then, the beamforming vectors at the base station (BS) and the transmission mode selection of the tiles of the IRS are jointly optimized for minimization of the BS transmit power taking into account the quality-of-service requirements of both non-linear energy harvesting receivers and information decoding receivers. For handling the resulting non-convex optimization problem, we apply a penalty-based method, successive convex approximation, and semidefinite relaxation to develop a computationally efficient algorithm which asymptotically converges to a locally optimal solution of the considered problem. Our simulation results show that the proposed scheme enables considerable power savings compared to two baseline schemes. Moreover, our results also illustrate that the advocated physics-based model and scalable optimization framework for large IRSs allows us to strike a balance between system performance and computational complexity, which is vital for realizing large IRS-assisted communication systems.