lect_21 - Numerical Marine Hydrodynamics • Finite Element...

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Unformatted text preview: Numerical Marine Hydrodynamics • Finite Element and Spectral Methods – Galerkin Methods – Computational Galerkin Methods • Spectral Methods • Finite Element Method – Finite Element Methods • Ordinary Differential Equation • Partial Differential Equations • Complex geometries Numerical Marine Hydrodynamics Lecture 21 2.29 Partial Differential Equations A,B and C Constants Hyperbolic Parabolic Elliptic y φ ( n ) (x,y 2 ) Quasi-linear PDE φ ( n ) (x 1 ,y) φ ( n ) (x 2 ,y) φ ( n ) (x,y 1 ) x Numerical Marine Hydrodynamics Lecture 21 2.29 Galerkin’s Method Boundary Conditions Test Function Solution Remainder Inner Product Galerkin’s Method Differential Equation y φ ( n ) (x,y 2 ) φ ( n ) (x 1 ,y) φ ( n ) (x 2 ,y) φ ( n ) (x,y 1 ) x Numerical Marine Hydrodynamics Lecture 21 2.29 Galerkin’s Method Example Differential Equation Boundary Conditions Power Series Boundary Condition Alternative Numerical Marine Hydrodynamics Lecture 21 2.29 Galerkin’s Method Example Remainder Complete Test Function Set Algebraic Equations N=3; d=zeros(N,1); m=zeros(N,N); exp_eq.m for k=1:N d(k)=1/k; for j=1:N m(k,j) = j/(j+k-1)-1/(j+k); end end a=inv(m)*d; y=ones(1,n); for k=1:N y=y+a(k)*x.^k end Numerical Marine Hydrodynamics Lecture 21 2.29 Galerkin’s Method Example L 2 Error N=3; d=zeros(N,1);...
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lect_21 - Numerical Marine Hydrodynamics • Finite Element...

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