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The Immersed Interface Method

https://doi.org/10.1137/1.9780898717464
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A fourth-order kernel-free boundary integral method for implicitly defined surfaces in three space dimensions
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Solving three-dimensional interface problems with immersed finite elements: A-priori error analysis
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A shallow Ritz method for elliptic problems with singular sources
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A discontinuity capturing shallow neural network for elliptic interface problems
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3D time-dependent scattering about complex shapes using high order difference potentials
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Kernel-free boundary integral method for two-phase Stokes equations with discontinuous viscosity on staggered grids
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Local randomized neural networks with finite difference methods for interface problems
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The immersed interface method for Helmholtz equations with degenerate diffusion
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Sharp Interface Algorithm for Large Density Ratio Incompressible Multiphase Magnetohydrodynamic Flows
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Scaling laws for drag of a compliant body in an incompressible viscous flow
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Interaction of two tandem deformable bodies in a viscous incompressible flow
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Machine-Learned Molecular Surface and Its Application to Implicit Solvent Simulations
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Improved Poisson–Boltzmann Methods for High-Performance Computing
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Simulations of Anodic Nanopore Growth Using the Smoothed Boundary and Level Set Methods
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Atomistic Insight on the Charging Energetics in Subnanometer Pore Supercapacitors
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Electric field assisted motion of a mercury droplet
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Exploring a charge-central strategy in the solution of Poisson's equation for biomolecular applications
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The least squares finite element method for elasticity interface problem on unfitted mesh
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Exact subgrid interface correction schemes for elliptic interface problems
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Augmented immersed finite element methods for some elliptic partial differential equations
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A fast high-order algorithm for the multiple cavity scattering
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Multidomain Legendre-Galerkin Chebyshev collocation least squares method for one-dimensional problems with two nonhomogeneous jump conditions
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A Fast Algorithm to Predict Cell Trajectories in Microdevices Using Dielectrophoresis
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The Method of Manufactured Solutions to Construct Flow Fields Across An Interface
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Selective surface normal estimation for volume rendering
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A variational approach to sparsity optimization based on Lagrange multiplier theory
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Dynamical systems techniques for enhancing microfluidic mixing
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Extended smoothed boundary method for solving partial differential equations with general boundary conditions on complex boundaries
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An unfitted hybridizable discontinuous Galerkin method for the Poisson interface problem and its error analysis
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Superconvergence of partially penalized immersed finite element methods
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Electrodeformation of vesicles suspended in a liquid medium
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A Novel T-G IFE Method for Two Dimensional Semi-Linear Elliptic Interface Problems Based on Coarse Grid Correction
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Optimal Absorption Design and Sensitivity of Eigenvalues
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An immersed finite element method for orthotropic interface problem
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A Boundary Difference Method for Electromagnetic Scattering Problems With Perfect Conductors and Corners
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Modified Finite Difference Methods for Reynold Equation With Film Thickness Discontinuity
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Interfacial gauge methods for incompressible fluid dynamics
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High-Order Grid-Characteristic Method for Systems of Hyperbolic Equations with Piecewise Constant Coefficients
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A Discontinuous Galerkin Method by Patch Reconstruction for Elliptic Interface Problem on Unfitted Mesh
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High Order Compact Schemes for Flux Type BCs
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