[HTML][HTML] Exploiting spatial symmetries for solving Poisson's equation
This paper presents a strategy to accelerate virtually any Poisson solver by taking
advantage of s spatial reflection symmetries. More precisely, we have proved the existence …
advantage of s spatial reflection symmetries. More precisely, we have proved the existence …
[ספר][B] Fast direct solvers for elliptic PDEs
PG Martinsson - 2019 - SIAM
In writing this book, I set out to create an accessible introduction to fast multipole methods
(FMMs) and techniques based on integral equation formulations. These are powerful tools …
(FMMs) and techniques based on integral equation formulations. These are powerful tools …
A high-order fast direct solver for surface PDEs
We introduce a fast direct solver for variable-coefficient elliptic PDEs on surfaces based on
the hierarchical Poincaré–Steklov method. The method takes as input an unstructured, high …
the hierarchical Poincaré–Steklov method. The method takes as input an unstructured, high …
[HTML][HTML] A particle-in-Fourier method with semi-discrete energy conservation for non-periodic boundary conditions
We introduce a novel particle-in-Fourier (PIF) scheme based on [1],[2] that extends its
applicability to non-periodic boundary conditions. Our method handles free space boundary …
applicability to non-periodic boundary conditions. Our method handles free space boundary …
A FFT accelerated high order finite difference method for elliptic boundary value problems over irregular domains
For elliptic boundary value problems (BVPs) involving irregular domains and Robin
boundary condition, no numerical method is known to deliver a fourth order convergence …
boundary condition, no numerical method is known to deliver a fourth order convergence …
Two-dimensional Fourier continuation and applications
This paper presents a fast “two-dimensional Fourier continuation”(2D-FC) method for
construction of biperiodic extensions of smooth nonperiodic functions defined over general …
construction of biperiodic extensions of smooth nonperiodic functions defined over general …
A fast integral equation method for the two-dimensional Navier-Stokes equations
The integral equation approach to partial differential equations (PDEs) provides significant
advantages in the numerical solution of the incompressible Navier-Stokes equations. In …
advantages in the numerical solution of the incompressible Navier-Stokes equations. In …
Adaptive quadrature by expansion for layer potential evaluation in two dimensions
When solving partial differential equations using boundary integral equation methods,
accurate evaluation of singular and nearly singular integrals in layer potentials is crucial. A …
accurate evaluation of singular and nearly singular integrals in layer potentials is crucial. A …
A fast, high-order scheme for evaluating volume potentials on complex 2D geometries via area-to-line integral conversion and domain map**s
While potential theoretic techniques have received significant interest and found broad
success in the solution of linear partial differential equations (PDEs) in mathematical …
success in the solution of linear partial differential equations (PDEs) in mathematical …
Partition of unity extension of functions on complex domains
We introduce an efficient algorithm, called partition of unity extension or PUX, to construct an
extension of desired regularity of a function given on a complex multiply connected domain …
extension of desired regularity of a function given on a complex multiply connected domain …