We design and analyze a coupling of discontinuous Galerkin finite element method with boundary to solve the Helmholtz equation variable coefficients in three dimensions. The is realized mortar that related an impedance trace on smooth interface. obtained has block structure nonsingular subblocks. prove quasi-optimality $$h$$ - $$p$$ -versions scheme, under threshold condition approximability pr...

Lumped element models, also known as, mass-spring-damper models, are widely used to simulate deformable objects because of their simplicity and computational efficiency. However, the parameters of lumped element models are typically determined in an ad hoc fashion through trial-and-error, as these models are not directly based on continuum mechanics of deformable objects. In this paper, an alte...

We present a dynamic simulation framework for topologychanging deformable objects. The objects are represented using tetrahedral meshes and deformations are governed by a corotational finite element approach for linear elasticity and plasticity. Geometric constraints are employed to efficiently handle topology changes in a unified way. Topology changes comprise fracturing and merging of deforma...

We present a load balancing technique for a boundary data accumulation algorithm for non-overlapping domain decompositions. The technique is used to speed up a parallel conjugate gradient algorithm with an algebraic multigrid preconditioner to solve a potential problem on an unstructured tetrahedral finite element mesh. The optimized accumulation algorithm significantly improves the performance...

We consider an algorithm called FEMWARP for warping tetrahedral finite element meshes that computes the warping using the finite element method itself. The algorithm takes as input a twoor three-dimensional domain defined by a boundary mesh (segments in one dimension or triangles in two dimensions) that has a volume mesh (triangles in two dimensions or tetrahedra in three dimensions) in its int...

Let $$\Omega $$ be a Lipschitz polyhedral (can nonconvex) domain in $${\mathbb {R}}^{3}$$ , and $$V_{h}$$ denotes the finite element space of continuous piecewise linear polynomials. On non-obtuse quasi-uniform tetrahedral meshes, we prove that projection $$R_{h}u$$ $$u \in H^{1}(\Omega ) \cap C({\overline{\Omega }})$$ (with $$R_{h} u$$ interpolating u at boundary nodes) satisfies $$\begin{alig...