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We present the AMPS algorithm, a finite element solution method that combinesprincipal submatrix updates and Schur complement techniques, well-suited forinteractive simulations of deformation and cutting of finite element meshes.Our approach features real-time solutions to the updated stiffness matrixsystems to account for interactive changes in mesh connectivity and boundaryconditions. Updates are accomplished by an augmented matrix formulation of thestiffness equations to maintain its consistency with changes to the underlyingmodel without refactorization at each timestep. As changes accumulate overmultiple simulation timesteps, the augmented solution algorithm enables tens orhundreds of updates per second. Acceleration schemes that exploit sparsity,memoization and parallelization lead to the updates being computed inreal-time. The complexity analysis and experimental results for this methoddemonstrate that it scales linearly with the problem size. Results for cuttingand deformation of 3D elastic models are reported for meshes with node countsup to 50,000, and involve models of astigmatism surgery and the brain.

AMPS: A Real-time Mesh Cutting Algorithm for Surgical Simulations