Gernot Beer's Advanced numerical simulation methods : from CAD data PDF

By Gernot Beer

ISBN-10: 1138026344

ISBN-13: 9781138026346

ISBN-10: 1315766310

ISBN-13: 9781315766317

This booklet is an wonderful, effortless to learn creation to complex numerical modeling. the purpose of the e-book is to steer the reader on a trip in the direction of the ‘holy grail’ of numerical simulation, particularly one with out the requirement of mesh iteration, that takes information without delay from CAD courses. in this trip readers will notice the wonderful thing about Non-uniform Rational B-Splines or NURBS and spot how good they're suited to describing geometry, detect how CAD courses paintings and the way their info can be utilized for simulation. The implementation of NURBS-based simulation is mentioned utilizing Finite aspect and Boundary aspect know-how. it is a hands-on e-book with emphasis on implementation and examples of programming in a better point language are given. it's been written for clients of simulation software program, to allow them to comprehend the advantages of this new know-how and insist development from a just a little conservative undefined, for software program builders, to allow them to see that it is a know-how with an immense destiny and for researchers, within the wish that it'll allure extra humans to paintings during this interesting new box.

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Example text

It can be observed that the higher order functions have significant negative values and exhibit oscillatory behavior. Figure 2 shows the derivatives for functions of order 2 and 3. 3, 1) with Lagrange polynomials of order p = 4. Two things can be observed: • • The curve goes through the given values of the function (nodal points). There is little control on what the curve does between the nodal points. 22 Advanced numerical simulation methods It turns out that these functions are not very well suited for numerical simulation.

It can be observed that the higher order functions have significant negative values and exhibit oscillatory behavior. Figure 2 shows the derivatives for functions of order 2 and 3. 3, 1) with Lagrange polynomials of order p = 4. Two things can be observed: • • The curve goes through the given values of the function (nodal points). There is little control on what the curve does between the nodal points. 22 Advanced numerical simulation methods It turns out that these functions are not very well suited for numerical simulation.

It is noted that the same result can be achieved if the parameter space is split into two and Bernstein polynomials are used for each subspace. We re-plot the function in Figure 7 with the modified knot vectors in Figures 16 and 17. It can be seen that the shape of the curve has been altered when compared to Bernstein polynomials. 5. Stage 1: Basis functions 31 Figure 16 Plot with the same control points as in Figure 7 but with knot vector 1, 1). 5, 1, 1, 1). NURBS The fact that we can control continuity and span of the functions makes them very powerful.

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Advanced numerical simulation methods : from CAD data directly to simulation results by Gernot Beer


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