AMPS swMATH ID: 36411 Software Authors: Yeung, Yu-Hong; Pothen, Alex; Crouch, Jessica Description: AMPS: Real-time mesh cutting with augmented matrices for surgical simulations. We present the augmented matrix for principal submatrix update (AMPS) algorithm, a finite element solution method that combines principal submatrix updates and Schur complement techniques, well-suited for interactive simulations of deformation and cutting of finite element meshes. Our approach features real-time solutions to the updated stiffness matrix systems to account for interactive changes in mesh connectivity and boundary conditions. Updates are accomplished by an augmented matrix formulation of the stiffness equations to maintain its consistency with changes to the underlying model without refactorization at each timestep. As changes accumulate over multiple simulation timesteps, the augmented solution algorithm enables tens or hundreds of updates per second. Acceleration schemes that exploit sparsity, memoization and parallelization lead to the updates being computed in real time. The complexity analysis and experimental results for this method demonstrate that it scales linearly with the number of nonzeros of the factors of the stiffness matrix. Results for cutting and deformation of three-dimensional (3D) elastic models are reported for meshes with up to 50 000 nodes, and involve models of surgery for astigmatism and the brain. Homepage: https://arxiv.org/abs/1811.00328 Keywords: cutting; deformable model; finite element; real-time; surgery simulation Related Software: CHOLMOD; Oblio; condest; MKL; SuiteSparse; AIM@SHAPE; Matlab Cited in: 1 Document Standard Articles 1 Publication describing the Software, including 1 Publication in zbMATH Year AMPS: real-time mesh cutting with augmented matrices for surgical simulations. Zbl 1474.65450Yeung, Yu-Hong; Pothen, Alex; Crouch, Jessica 2020 Cited by 3 Authors 1 Crouch, Jessica 1 Pothen, Alex 1 Yeung, Yu-Hong Cited in 1 Serial 1 Numerical Linear Algebra with Applications Cited in 4 Fields 1 Partial differential equations (35-XX) 1 Numerical analysis (65-XX) 1 Mechanics of deformable solids (74-XX) 1 Biology and other natural sciences (92-XX) Citations by Year