In scientific computation and simulation, the method of fundamental solutions (MFS) is a technique for solving partial differential equations based on using the fundamental solution as a basis function. The MFS was developed to overcome the major drawbacks in the boundary element method (BEM) which also uses the fundamental solution to satisfy the governing equation. Consequently, both the MFS and the BEM are of a boundary discretization numerical technique and reduce the computational complexity by one dimensionality and have particular edge over the domain-type numerical techniques such as the finite element and finite volume methods on the solution of infinite domain, thin-walled structures, and inverse problems.
In contrast to the BEM, the MFS avoids the numerical integration of singular fundamental solution and is an inherent meshfree method. The method, however, is compromised by requiring a controversial fictitious boundary outside the physical domain to circumvent the singularity of fundamental solution, which has seriously restricted its applicability to real-world problems. But nevertheless the MFS has been found very competitive to some application areas such as infinite domain problems.
The MFS is also known by different names in the literature, including the charge simulation method, the superposition method, the desingularized method, the indirect boundary element method and the virtual boundary element method.
and 24 Related for: Method of fundamental solutions information
simulation, the methodoffundamentalsolutions (MFS) is a technique for solving partial differential equations based on using the fundamentalsolution as a basis...
for solutionsof partial differential equations. There is correspondingly a vast amount of modern mathematical and scientific research on methods to numerically...
basis function Methodoffundamentalsolutions Boundary knot method Boundary particle method Singular boundary method Modified Kansa method E. J. Kansa,...
singular boundary method (SBM) belongs to a family of meshless boundary collocation techniques which include the methodoffundamentalsolutions (MFS), boundary...
knot method is different from the other methods based on the fundamentalsolutions, such as boundary element method, methodoffundamentalsolutions and...
Semi-implicit Method Methodoffundamentalsolutions (MFS) — represents solution as linear combination offundamentalsolutions Variants of MFS with source...
basis/kernel functions. Like the methodoffundamentalsolutions (MFS), the numerical solution is approximated by a linear combination of double layer kernel functions...
does not have a solution in R {\displaystyle \mathbb {R} } (the solutions are the imaginary units i and –i). While the real solutionsof real equations...
basic explicit method for numerical integration of ordinary differential equations and is the simplest Runge–Kutta method. The Euler method is named after...
boundary element method, no fundamental differential solution is required. The S-FEM, Smoothed Finite Element Methods, is a particular class of numerical simulation...
The scientific method is an empirical method for acquiring knowledge that has characterized the development of science since at least the 17th century...
the puzzle has 12 solutions. These are called fundamentalsolutions; representatives of each are shown below. A fundamentalsolution usually has eight...
do not have closed form solutions. Instead, solutions can be approximated using numerical methods. Many fundamental laws of physics and chemistry can...
such as the methodoffundamentalsolution (MFS), boundary knot method (BKM), regularized meshless method (RMM), singular boundary method (SBM), and Trefftz...
540–558. Craddock, M. & Platen, E. (2004). Symmetry group methods for fundamentalsolutions. Journal of Differential Equations, 207 (2), 285–302. Platen, E...
chemistry: fundamentals. pp. 60. ISBN 978-0387260617. Bradford, M.M. (1976), "Rapid and sensitive method for the quantitation of microgram quantities of protein...
variable is an equation of the form a x 3 + b x 2 + c x + d = 0 {\displaystyle ax^{3}+bx^{2}+cx+d=0} in which a is nonzero. The solutionsof this equation are...
1950s Schwarz's method was generalized in the theory of partial differential equations to an iterative method for finding the solutionof an elliptic boundary...
possible to find solutions via integrating factors or undetermined coefficients with considerably less effort, although those methods leverage heuristics...
The methodof least squares is a parameter estimation method in regression analysis based on minimizing the sum of the squares of the residuals (a residual...
proof of the fundamental theorem of algebra. He presented his solution, which amounts in modern terms to a combination of the Durand–Kerner method with...
there are either two real solutions, or a single real double root, or two complex solutions that are complex conjugates of each other. A quadratic equation...