The proposed low-rank multipatch method can be extended to accommodate more general boundary conditions by modifying the construction of the isogeometric spaces and the associated linear systems. In the conforming case, the method relies on the assumption that the meshes are conforming at the patch interfaces, which simplifies the identification of basis functions across patches. To handle non-conforming boundary conditions, one could introduce additional subdomains that account for Neumann boundary conditions or mixed boundary conditions.
One approach is to define auxiliary subdomains that encapsulate the Neumann degrees of freedom, allowing for the representation of the solution space that includes both Dirichlet and Neumann conditions. This can be achieved by adjusting the tensor product spline spaces to ensure that the basis functions vanish on the Dirichlet boundaries while still allowing for non-zero values on Neumann boundaries.
Moreover, the merging of local spline spaces can be adapted to ensure that the resulting space is still a tensor product space, even when the boundary conditions are not homogeneous. This may involve using projection techniques to enforce the boundary conditions appropriately. By carefully constructing the geometry mappings and ensuring that the resulting spline spaces respect the boundary conditions, the low-rank multipatch method can be effectively generalized to handle a wider variety of boundary conditions.