Radio-frequency (RF) beams in the electron cyclotron resonance (ECR) frequency range are used to heat plasma and to drive current in most fusion devices such as Tokamaks, Stellarators and RFPs. RF power absorption at fundamental electron cyclotron resonance or its harmonics and damping of mode converted electron Bernstein waves are being studied as the main plasma heating and control methods in future fusion reactors. RF technologies in plasma and other dielectric media also have numerous applications beyond fusion. RF heating and plasma creation is used in Helicon plasma sources, in ECR ion sources, in inductively and capacitively coupled plasma discharges, in the semiconductor industry and medical applications, in RF communications and remote sensing, in development of radar systems. Also, the physics of waves propagation in a hot plasma is a subject of ongoing academic research. However, an accurate practical modeling of RF beams in plasma devices is very limited by the large spatial resolution, computer memory and CPU time requirements. Based on our recently developed hybrid iterative approach for solving wave equations in frequency domain, we propose to develop 3D full wave iterative RF beams simulation tool which will be used for 3D modeling of ECRH RF beams in fusion devices and for full wave simulations of RF beams propagating in different dielectric media for industrial and military applications. We propose to use dynamically adapted grid with simulation points covering only the volume of the beam to reduce the memory and CPU time requirements of simulations. The tool will use the power of multiprocessing and it will utilize modern parallel libraries. The capability to use first principles nonlocal hot plasma dielectric response model will be part of the proposed tool as it is needed in fusion and in many industrial applications such as Tokamaks, Stellarators, Torsatrons, Reversed Field Pinches, Helicon sources and ECRIS devices. Our final product will be a cutting- edge turnkey RF simulation tool for these applications. In Phase I we will perform research and development to: 1) Examine feasibility of using the hybrid iterative algorithm for solving wave equations in 3D geometry on dynamically adapted grid for modeling 3D RF beams; 2) Examine parallel scalability of this algorithm to large-scale parallel systems.The code will be used: in the design, operation and performance assessment of radio-frequency systems in existing and planned fusion devices, industrial radio-frequency plasma devices, electron cyclotron ion sources, in basic research on plasma waves, in communications, remote sensing and military applications.