# Questions tagged [reference-request]

This tag is for requests for books, papers, and citations.

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39 views

Well, actually my goal is solving ODEs with Explicit Adam-Bashforth-Moulton Seventh Order Steps with matlab code. I'm searching in the internet, and i can't find about the formula (Sadly). But if ...
296 views

### The Formula of Explicit Runge-Kutta Fourteen order

I need an explicit Runge-Kutta 14th order formula. If you know about some reference that discusses at least 10th order (or higher, since I'm looking for the 14th) of Runge-Kutta and there is ...
47 views

### Methods to approximate obective function gradients from point cloud

Problem statement: Assume that I have an objective function $f(x)$ which takes as input a $D$-dimensional vector $x\in\mathbb{R}^D$, and that $f(x)$ is sufficiently smooth. Assume further that I ...
21 views

### Truncated power series algebra implementation

1) I am looking for references for an efficient implementation and usage of TPSA. What sources exist besides Berz's 1989 original paper and the incomplete chapter in Dragt's book? 2) Are there ...
48 views

### What is the fastest algorithm for computing log determinant?

I am diving into some literature to understand which is the best algorithm for computing the log-determinant of a PSD matrix. So far I have found the following two papers: Large-scale Log-...
134 views

### Consumer hardware for scientific computing?

I'm interested in problems around probability, statistics, and statistical mechanics, and often I find it useful to perform simulations to get some sense of the underlying phenomena. Example ...
62 views

### How to approach geographic data interpolation by distance?

let's say I have a set of geographic locations (lat, lng) resulting from a query. Those locations have some kind of internal ranking, my set is sorted by this number in a descending order. Now I'm ...
97 views

### “Geometry of ill-conditioning” for least-squares problems

It is an idea that dates back to Demmel, 1987 that the condition number of a problem is often related to the distance to the closest ill-posed problems. In Section 3 of the above paper, the author ...
90 views

### Simulating advection - diffusion problem in a network of 1D pipe

I'm interested in solving the following advection-diffusion system in a 1D network of pipes. $$\frac{\partial C}{\partial t} = D\frac{\partial ^2 C}{\partial x^2} - v\frac{\partial C}{\partial x}$$ ...
26 views

### Book Recommendation: Analysis and design of mechanistic models - such as pharmacokinetics or hydrology models

I have been looking at an interesting book "Pharmacokinetic-Pharmacodynamic Modeling and Simulation" by Peter Bonate on pharmacokinetic models: the models of how medical drugs work their way through ...
87 views

### Are there well-known methods for navigating on kd-trees?

When you have a mesh, there are many well-known methods to navigate it, as for example using a half-edge data structure, that allows easy circulation around faces and vertices. Are there similar ...
88 views

### Reference request: Riks method (Nonlinear FEM)

I'm struggling to find a good detailed reference explaining the Arc-length method or, more generally, Riks method and its derivations. I looked for the classical books in nonlinear mechanics (the ones ...
42 views

### Classification of multiobjective optimization algorithms

I am looking for a good (canonical?) overview paper(s)/book(s) on the classification of multiobjective optimization algorithms. I am focused on obtaining a representative set of Pareto optimal ...
75 views

### Good reference on the implementation and limitations of SDIRK methods

For the solution of many PDE, implicit high-order time integration schemes are required. I am specifically interested in schemes that do not require a constant time step. I am well acquainted with ...
44 views

### References to solve system of differential equations which describe the evolution of sandpile surface using the finite element method

I want to solve the following nonlinear system in 1D \begin{cases} \dot{R} + v \frac{\partial R }{\partial x} - \frac{\partial }{\partial x}\left( D \frac{\partial R }{\partial x} \right) -\Gamma =...
98 views

### Original paper on the augmented Lagrangian method in FEM

I am writing a paper in which I want to cite the earliest reference to the augmented Lagrangian method in FEM. For the pure Lagrangian method in FEM, the classical work of Babuška  is the original ...
43 views

### Is it Grid/Cluster/Cloud Computing? How are those terms defined?

There are three very connected and widely used terms: Grid and grid computing Cluster and cluster computing Cloud and cloud computing In many situations, it is not obvious which term to use, as I ...
51 views

### Reverse automatic differentiation and integration

In Symplectic Runge-Kutta schemes for adjoint equations, automatic differentiation, optimal control and more Sanz Serna writes: It is well known that the reverse mode of differentiation implies ...
106 views

### References for the nonlinear reaction-diffusion equation using Finite Element Methods

I want to study how to solve the following PDE \begin{cases} -\nabla \cdot(\ k(x,y) \ \nabla u \ ) + \beta(x,y)\ u^2 = f(x,y), \ (x,y) \in \Omega \subset \mathbb{R^2} \\ \hspace{0.5cm} u = ...
68 views

### Good references for dual-weighted residual (DWR) method for goal-oriented adaptive mesh refinement (AMR)

Can anyone help me with good references (books or papers) where I can learn about dual-weighted residual (DWR) method for goal-oriented adaptive mesh refinement (AMR)?
112 views

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### What good are hard-sphere event-driven molecular dynamics simulations in the face of chaos?

Simple hard-sphere dynamical systems can exhibit chaotic dynamics. Due to finite-precision arithmetic when implemented on a computer, the presence of chaos implies that for a given set of initial data,...
355 views

### For noisy or fine-structured data, are there better quadratures than the midpoint rule?

Only the first two sections of this long question are essential. The others are just for illustration. Background Advanced quadratures such as higher-degree composite Newton–Cotes, Gauß–Legendre, ...
75 views

### References in Scientific Computation for a Computer Science Undergrad? [duplicate]

TLDR: What references and pre-requisites are necessary for a Computer Science Undergraduate to get ready for a Masters and Career in Scientific Computation / Computational X For a Computer Science ...
19 views

### Implementation of a ratio with a well-defined limit

I'm implementing a function $f(x_1, x_2, \dots x_n)$ given by the ratio of two closed form equations. $$f(x_1, x_2, \dots, x_n) = \frac{g(x_1, x_2, \dots, x_n)}{h(x_1, x_2, \dots, x_n)}$$ ...
2k views

### Physics Simulation in C++

OK, I know a bit of C++ (very basic syntax), and I want to do physics simulation in C++, like stuff like (also the things mentioned here): Ripples and waves over a 2-d surface Vibrating string/...
354 views

### How to directly compute the inverse of an ill-conditioned dense matrix

I know that it is generally a bad idea to compute the inverse matrix directly. However, if it is necessary to compute the inverse of an ill-conditioned invertible dense matrix, then what can I try? ...
87 views

### Computation of the heat kernel from Brownian motion

This question is rather simple but I have some difficulties to find code. Let us suppose that I wrote a routine, in a given language, that computes the evolution of a particle doing Brownian motion in ...
152 views

### Analysis and numerical methods for PDEs arising in industrial problems

Assume some basic knowledge of numerical methods for PDEs, acquired through A. Quarteroni's Numerical models for differential problems. I'm looking for a reference to get started on the analysis of ...