Adaptive Nonlinear Finite Elements for Deformable Body Simulation Using Dynamic Progressive Meshes

Abstract

Realistic behavior of deformable objects is essential for many applications such as simulation for surgical training. Existing techniques of deformable modeling for real time simulation have either used approximate methods that are not physically accurate or linear methods that do not produce reasonable global behavior. Nonlinear finite element methods (FEM) are globally accurate, but conventional FEM is not real time. In this paper, we apply nonlinear FEM using mass lumping to produce a diagonal mass matrix that allows real time computation. Adaptive meshing is necessary to provide sufficient detail where required while minimizing unnecessary computation. We propose a scheme for mesh adaptation based on an extension of the progressive mesh concept, which we call dynamic progressive meshes.

An efficient large deformation method using domain decomposition

“…There are many approaches for quickly solving the discretized equations using adaptive methods to avoid wasting time on minor details. Some recently proposed representative work are [18][19][20][21]. Capell et al proposed a multiresolution framework for dynamic simulation using volumetric subdivision [18].…”

“…By adaptively refining the basis functions, Grinspun et al proposed another simple framework for adaptive simulation [19], called CHARMS. Wu et al [20] and Debunne et al [21] developed other kinds of adaptive methods using progressive meshes and LOD tetrahedral meshes. Debunne et al also took adaptive time steps during simulation [21] to further avoid unnecessary computation.…”

Characterization of Intra-abdominal Tissues from in vivo Animal Experiments for Surgical Simulation

“…Recently, several attempts have been made to simulate nonlinear deformations of soft tissues in surgical simulations [13]. Furthermore, the addition of haptic feedback to the simulator necessitates a nonlinear tissue model for more realistic force feedback.…”

Physically-Based Surface Texture Synthesis Using a Coupled Finite Element System

“…The deformation field between 3D images was computed by locally minimizing the sum of the squared differences between the images to be matched [11]. Nonlinear FEM using mass lumping was applied to produce a diagonal mass matrix that allows real time computation, and dynamic progressive meshes were generated to provide detailed information while minimizing computation [21].…”

“…Then the diffusion tensor is defined as (19) where N(x) is the normal component of z, and g(s) is (20) λ is a given parameter which detects sharp features. After the spatial and time discretization of the weak form, Equation (18) can be rewritten as follows, (21) where ν is the test function, τ is the time step, and n is the step number. The mass matrix, the stiffness matrix and the force vector are as follow,…”