Jacob J. Koester's research while affiliated with Sandia National Laboratories and other places
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Publications (6)
An efficient and momentum conserving algorithm for enforcing contact between solid bodies is proposed. Previous advances in the material point method (MPM) led to a fast and simple, but potentially momentum violating, strategy for enforcing contact. This was achieved through a combination of velocity transfers between background and foreground grid...
We introduce an immersed meshfree formulation for modeling heterogeneous materials with flexible non-body-fitted discretizations, approximations, and quadrature rules. The interfacial compatibility condition is imposed by a volumetric constraint, which avoids a tedious contour integral for complex material geometry. The proposed immersed approach i...
This report summarizes the work performed under a one-year LDRD project aiming to enable accurate and robust numerical simulation of partial differential equations for meshes that are of poor quality.
Traditional finite element methods use the mesh to both discretize the geometric domain and to define the finite element shape functions. The latter...
The Waste Isolation Pilot Plant (WIPP) is a geologic repository for defense-related nuclear waste. If left undisturbed, the virtually impermeable rock salt surrounding the repository will isolate the nuclear waste from the biosphere. If humans accidentally intrude into the repository in the future, then the likelihood of a radionuclide release to t...
We propose new projection methods for treating near-incompressibility in small and large deformation elasticity and plasticity within the framework of particle and meshfree methods. Using the \(\overline{\mathbf {B}}\) and \(\overline{\mathbf {F}}\) techniques as our point of departure, we develop projection methods for the conforming reproducing k...
Window functions provide a base for the construction of approximation functions in many meshfree methods. They control the smoothness and extent of the approximation functions and are commonly defined using Euclidean distances which helps eliminate the need for a meshed discretization, simplifying model development for some classes of problems. How...
Citations
... In cases such as these, the updated Lagrangian formulation can be used for the weak form, and the RK shape functions and their gradients must be recomputed following the material points with updated neighbors at each time step to reflect the new free surface topology in the deformed configuration. This formulation is called semi-Lagrangian RKPM (SL-RK) [56,57] and has been successfully applied to an array of severe deformation problems such as fracture and fragmentation [53,54,57,58], earth-moving and landslides [57,59,60], and rock collapse and reconsolidation [61]. The major drawback to this formulation, however, is its high computational cost. ...
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... The boundary conditions or fluxes in this technique are interpolated using the Cartesian grid points and this leads to the increase in the stencil width for the grid points located close to the boundary (the numerical techniques developed in [19-21, 33, 34] provide the second order of accuracy for the global solution). The development of different numerical techniques (finite difference method, immersed finite element method, immersed meshfree method) for statics elasticity interface problems with unfitted meshes were recently reported in [39][40][41]. ...
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... We replicate the problem setup in [40] with a similar mesh design as in the previous section. The experimental investigations for this classical benchmark problem may be traced back to [41]. ...
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... In this case, the kernel function Φ a has a brick support shape. In addition, in [50] RK kernel functions defined on triangulations are employed. In [18], an RKPM-based open-source software is developed and the implementation of different kernel functions for RKPM are discussed in detail. ...
