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The ideal Magnetohydrodynamics (MHD) equations are challenging because oneneeds to maintain the divergence free condition, $\nabla \cdot \Bv = 0$. Manynumerical methods have been developed to enforce this condition. In this work,we further our work on mesh aligned constrained transport by developing a newkernel based approach for the vector potential in 2D and 3D. The approach forsolving the vector potential is based on the method of lines transpose and isA-stable, eliminating the need for diffusion limiters needed in our previouswork in 3D. The work presented here is an improvement over the previous methodin the context of problems with strong shocks due to the fact that we couldeliminate the diffusion limiter that was needed in our previous version ofconstrained transport. The method is robust and has been tested on the 2D and3D cloud shock, blast wave and field loop problems.

A Kernel Based High Order "Explicit" Unconditionally Stable Constrained Transport Method for Ideal Magnetohydrodynamics