Uncovering Mechanisms of Coronal Magnetism via Advanced 3D Modeling of Flares and Active Regions

The coming decade will see the routine use of solar data of unprecedented spatial and spectral resolution, time cadence, and completeness. To capitalize on the new (or soon to be available) facilities such as SDO, ATST and FASR, and the challenges they present in the visualization and synthesis of multi-wavelength datasets, we propose that realistic, sophisticated, 3D active region and flare modeling is timely and critical, and will be a forefront of coronal studies over the coming decade. To make such modeling a reality, a broad, concerted effort is needed to capture the wealth of information resulting from the data, develop a synergistic modeling effort, and generate the necessary visualization, interpretation and model-data comparison tools to accurately extract the key physics.